X 


THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

LOS  ANGELES 


SOUND 


By  John    Tyndall 


D.    APPLETON    AND     COMPANY 
NEW   YORK   AND    LONDON 


Authorized  Edition. 


Limited  to  one  thousand  copies, 
of  which  this  is  No 


UMART 


1*7$- 

(£0  tl)e 


MY  FRIEND  RICHARD  DA  WES, 

LATE  DEAN  OF  HEREFORD, 

THIS  BOOK   IS   DEDICATED. 

J.  T. 


J 645141 


PKEFACE 

TO 

THE  THIRD  EDITION. 


IN  preparing  tliis  new  edition  of  "  Sound,"  I  have 
carefully  gone  over  the  last  one;  amended,  as  far  as 
possible,  its  defects  of  style  and  matter,  and  paid  at  the 
same  time  respectful  attention  to  the  criticisms  and 
suggestions  which  the  former  editions  called  forth. 

The  cases  are  few  in  which  I  have  been  content  to  re- 
produce what  I  have  read  of  the  works  of  acousticians.  I 
have  sought  to  make  myself  experimentally  familiar  with 
the  ground  occupied;  trying,  in  all  cases,  to  present  the 
illustrations  in  the  form  and  connection  most  suitable  for 
educational  purposes. 

Though  bearing,  it  may  be,  an  undue  share  of  the  im- 
perfection which  cleaves  to  all  human  effort,  the  work  has 
already  found  its  way  into  the  literature  of  various  nations 
of  diverse  intellectual  standing.  Last  year,  for  example, 
a  new  German  edition  was  published  "  under  the  special 
supervision  "  of  Helmholtz  and  Wiedemann.  That  men 
so  eminent,  and  so  overladen  with  official  duties,  should 
add  to  these  the  labor  of  examining  and  correcting  every 
proof-sheet  of  a  work  like  this,  shows  that  they  consider 
it  to  be  what  it  was  meant  to  be — a  serious  attempt  to  im- 


6  PREFACE. 

prove  the  public  knowledge  of  science.  It  is  especially 
gratifying  to  me  to  be  thus  assured  that  not  in  England 
alone  has  the  book  met  a  public  want,  but  also  in  that 
learned  land  to  which  I  owe  my  scientific  education. 

Before  me,  on  the  other  hand,  lie  two  volumes  of  fools- 
cap size,  curiously  stitched,  and  printed  in  characters  the 
meaning  of  which  I  am  incompetent  to  penetrate.  Here 
and  there,  however,  I  notice  the  familiar  figures  of  the  for- 
mer editions  of  "  Sound."  For  these  volumes  I  am  in- 
debted to  Mr.  John  Fryer,  of  Shanghai,  who,  along  with 
them,  favored  me,  a  few  weeks  ago,  with  a  letter  from 
which  the  following  is  an  extract:  "  One  day,"  writes  Mr. 
Fryer,  "  soon  after  the  first  copy  of  your  work  on  Sound 
reached  Shanghai,  I  was  reading  it  in  my  study,  when  an 
intelligent  official,  named  Hsii-chung-hu,  noticed  some  of 
the  engravings  and  asked  me  to  explain  them  to  him.  He 
became  so  deeply  interested  in  the  subject  of  Acoustics, 
that  nothing  would  satisfy  him  but  to  make  a  translation. 
Since,  however,  engineering  and  other  works  were  then 
considered  to  be  of  more  practical  importance  by  the 
higher  authorities,  we  agreed  to  translate  your  work 
during  our  leisure  time  every  evening,  and  publish  it 
separately  ourselves.  Our  translation,  however,  when 
completed,  and  shown  to  the  higher  officials,  so  much  inter- 
ested them,  and  pleased  them,  that  they  at  once  ordered 
it  to  be  published  at  the  expense  of  the  Government,  and 
sold  at  cost  price.  'The  price  is  four  hundred  and  eighty 
copper  cash  per  copy,  or  about  one  shilling  and  eightpence. 
This  will  give  you  an  idea  of  the  cheapness  of  native 
printing." 


PREFACE.  7 

Mr.  Fryer  adds  that  his  Chinese  friend  had  no  diffi- 
culty in  grasping  every  idea  in  the  book. 

The  new  matter  of  greatest  importance  which  has  been 
introduced  into  this  edition  is  an  account  of  an  investiga- 
tion which,  during  the  two  past  years,  I  have  had  the  honor 
of  conducting  in  connection  with  the  Elder  Brethren  of 
the  Trinity  House.  Under  the  title  "  Researches  on  the 
Acoustic  Transparency  of  the  Atmosphere,  in  Relation  to 
the  Question  of  Fog-signaling,"  the  subject  is  treated  in 
Chapter  VII.  of  this  volume.  It  was  only  by  Govern- 
mental appliances  that  such  an  investigation  could  have 
been  made;  and  it  gives  me  pleasure  to  believe  that  not 
only  have  the  practical  objects  of  the  inquiry  been  secured, 
but  that  a  crowd  of  scientific  errors,  which  for  more  than 
a  century  and  a  half  have  surrounded  this  subject,  have 
been  removed,  their  place  being  now  taken  by  the  sure 
and  certain  truth  of  Nature.  In  drawing  up  the  account 
of  this  laborious  inquiry,  I  aimed  at  linking  the  observa- 
tions so  together,  that  they  alone  should  offer  a  substantial 
demonstration  of  the  principles  involved.  Further  labors 
enabled  me  to  bring  the  whole  inquiry  within  the  firm 
grasp  of  experiment;  and  thus  to  give  it  a  certainty  which, 
without  this  final  guarantee,  it  could  scarcely  have  enjoyed. 

Immediately  after  the  publication  of  the  first  brief  ab- 
stract of  the  investigation,  it  was  subjected  to  criticism. 
To  this  I  did  not  deem  it  necessary  to  reply,  believing 
that  the  grounds  of  it  would  disappear  in  presence  of  the 
full  account.  The  only  opinion  to  which  I  thought  it 
right  to  defer  was  to  some  extent  a  private  one,  commu- 


8  PREFACE. 

nicated  to  me  by  Prof.  Stokes.  He  considered  that  I  had, 
in  some  cases,  ascribed  too  exclusive  an  influence  to  the 
mixed  currents  of  aqueous  vapor  and  air,  to  the  neglect 
of  differences  of  temperature.  That  differences  of  tem- 
perature, when  they  come  into  play,  are  an  efficient  cause 
of  acoustic  opacity,  I  never  doubted.  In  fact,  aerial  re- 
flection arising  from  this  cause  is,  in  the  present  inquiry, 
for  the  first  time  made  the  subject  of  experimental  demon- 
stration. What  the  relative  potency  of  differences  of  tem- 
perature and  differences  due  to  aqueous  vapor,  in  the  cases 
under  consideration,  may  be,  I  do  not  venture  to  state; 
but  as  both  are  active,  I  have,  in  Chapter  VII.,  referred 
to  them  jointly  as  concerned  in  the  production  of  those 
"  acoustic  clouds  "  to  which  the  stoppage  of  sound  in  the 
atmosphere  is  for  the  most  part  due. 

Subsequently,  however,  to  the  publication  of  the  full 
investigation  another  criticism  appeared,  to  which,  in  con- 
sideration of  its  source,  I  would  willingly  pay  all  respect 
and  attention.  In  this  criticism,  which  reached  me  first 
through  the  columns  of  an  American  newspaper,  differ- 
ences in  the  amounts  of  aqueous  vapor,  and  differences  of 
temperature  are  alike  denied  efficiency  as  causes  of  acous- 
tic opacity.  At  a  meeting  of  the  Philosophical  Society  of 
Washington  the  emphatic  opinion  had,  it  was  stated,  been 
expressed  that  I  was  wrong  in  ascribing  the  opacity  of  the 
atmosphere  to  its  flocculence,  the  really  efficient  cause  be- 
ing refraction.  This  view  appeared  to  me  so  obviously 
mistaken  that  I  assumed,  for  a  time,  the  incorrectness  of 
the  newspaper  account. 


PREFACE.  9 

Recently,  however,  I  have  been  favored  with  the  "  Re- 
port of  the  United  States  Lighthouse  Board  for  1874,"  in 
which  the  account  just  referred  to  is  corroborated.  A 
brief  reference  to  the  Report  will  here  suffice.  Major 
Elliott,  the  accomplished  officer  and  gentleman  referred  to 
at  page  261,  had  published  a  record  of  his  visit  of  inspec- 
tion to  this  country,  in  which  he  spoke,  with  a  perfectly 
enlightened  appreciation  of  the  facts,  of  the  differences 
between  our  system  of  lighthouse  illumination  and  that 
of  the  United  States.  He  also  embodied  in  his  Report 
some  account  of  the  investigation  on  fog-signals,  the  initia- 
tion of  which  he  had  witnessed,  and  indeed  aided,  at  the 
South  Foreland. 

On  this  able  Report  of  their  own  officer  the  Lighthouse 
Board  at  Washington  make  the  following  remark:  "  Al- 
though this  account  is  interesting  in  itself  and  to  the  public 
generally,  yet,  being  addressed  to  the  Lighthouse  Board  of 
the  United  States,  it  would  tend  to  convey  the  idea  that 
the  facts  which  it  states  were  new  to  the  Board,  and  that 
the  latter  had  obtained  no  results  of  a  similar  kind;  while 
a  reference  to  the  appendix  to  this  report1  will  show  that 
the  researches  of  our  Lighthouse  Board  have  been  much 
more  extensive  on  this  subject  than  those  of  the  Trinity 
House,  and  that  the  latter  has  established  no  facts  of  prac- 
tical importance  which  had  not  been  previously  observed 
and  used  by  the  former." 

The  "  appendix  "  here  referred  to  is  from  the  pen  of 
the  venerable  Prof.  Joseph  Henry,  chairman  of  the  Light- 

1  It  will  be  borne  in  mind  that  the  Washington  Appendix  was  pub- 
lished nearly  a  year  after  my  Report  to  the  Trinity  House. 


10  PREFACE. 

house  Board  at  Washington.  To  his  credit  be  it  recorded 
that  at  a  very  early  period  in  the  history  of  fog-signaling 
Prof.  Henry  reported  in  favor  of  Daboll's  trumpet,  though 
he  was  opposed  by  one  of  his  colleagues  on  the  ground 
that  "  fog-signals  were  of  little  importance,  since  the  mari- 
ner should  know  his  place  by  the  character  of  his  sound- 
ings." In  the  appendix,  he  records  the  various  efforts 
made  in  the  United  States  with  a  view  to  the  establish- 
ment of  fog-signals.  He  describes  experiments  on  bells, 
and  on  the  employment  of  reflectors  to  reinforce  their 
sound.  These,  though  effectual  close  at  hand,  were  found 
to  be  of  no  use  at  a  distance.  He  corrects  current  errors 
regarding  steam-whistles,  which  by  some  inventors  were 
thought  to  act  like  ringing  bells.  He  cites  the  opinion  of 
the  Rev.  Peter  Ferguson,- that  sound  is  better  heard  in  fog 
than  in  clear  air.  This  opinion  is  founded  on  observations 
of  the  noise  of  locomotives;  in  reference  to  which  it  may 
be  said  that  otherj  have  drawn  from  similar  experiments 
diametrically  opposite  conclusions.  On  the  authority  of 
Captain  Keeney  he  cites  an  occurrence,  "  in  the  first  part 
of  which  the  captain  was  led  to  suppose  that  fog  had  a 
marked  influence  in  deadening  sound,  though  in  a  subse- 
quent part  he  came  to  an  opposite  conclusion."  Prof. 
Henry  also  describes  an  experiment  made  during  a  fog  at 
Washington,  in  which  he  employed  "  a  small  bell  rung  by 
clock-work,  the  apparatus  being  the  part  of  a  moderator 
lamp,  intended  to  give  warning  to  the  keepers  when  the 
supply  of  oil  ceased.  The  result  of  the  experiment  was, 
he  affirms,  contrary  to  the  supposition  of  absorption  of 
the  sound  by  the  fog."  This  conclusion  is  not  founded 


PREFACE.  11 

on  comparative  experiments,  but  on  observations  made 
in  the  fog  alone;  for,  adds  Prof.  Henry,  "the  change 
in  the  condition  of  the  atmosphere,  as  to  temperature  and 
the  motion  of  the  air,  before  the  experiment  could  be  re- 
peated in  clear  weather,  rendered  the  result  not  entirely 
satisfactory." 

This,  I  may  say,  is  the  only  experiment  on  fog  which  I 
have  found  recorded  in  the  appendix. 

In  1867  the  steam-siren  was  mounted  at  Sandy  Hook, 
and  examined  by  Prof.  Henry.  He  compared  its  action 
with  that  of  a  Daboll  trumpet,  employing  for  this  purpose 
a  stretched  membrane  covered  with  sand,  and  placed  at 
the  small  end  of  a  tapering  tube  which  concentrated  the 
sonorous  motion  upon  the  membrane.  The  siren  proved 
most  powerful.  "  At  a  distance  of  50,  the  trumpet  pro- 
duced a  decided  motion  of  the  sand,  while  the  siren  gave 
a  similar  result  at  a  distance  of  58."  Prof.  Henry  also 
varied  the  pitch  of  the  siren,  and  found  that  in  associa- 
tion with  its  trumpet  400  impulses  per  second  yielded 
the  maximum  sound;  while  the  best  result  with  the  un- 
aided siren  was  obtained  when  the  impulses  were  360  a 
second.  Experiments  were  also  made  on  the  influence  of 
pressure;  from  which  it  appeared  that  when  the  pressure 
varied  from  100  Ibs.  to  20  Ibs.,  the  distance  reached  by 
the  sound  (as  determined  by  the  vibrating  membrane) 
varied  only  in  the  ratio  of  61  to  51.  Prof.  Henry  also 
showed  the  sound  of  the  fog-trumpet  to  be  independent 
of  the  material  employed  in  its  construction;  and  he 
furthermore  observed  the  decay  of  the  sound  when  the 
angular  distance  from  the  axis  of  the  instrument  was  in- 


12  PREFACE. 

creased.  Further  observations  were  made  by  Prof.  Henry 
and  his  colleagues  in  August,  1873,  and  in  August  and 
September,  1874.  In  the  brief  but  interesting  account 
of  these  experiments  a  hypothetical  element  appears,  which 
is  absent  from  the  record  of  the  earlier  observations. 

It  is  quite  evident  from  the  foregoing  that,  in  regard 
to  the  question  of  fog-signaling,  the  Lighthouse  Board 
of  Washington  have  not  been  idle.  Add  to  this  the  fact 
that  their  eminent  chairman  gives  his  services  gratuitously, 
conducting  without  fee  or  reward  experiments  and  obser- 
vations of  the  character  here  revealed,  and  I  think  it  will 
be  conceded  that  he  not  only  deserves  well  of  his  own 
country,  but  also  sets  his  younger  scientific  contempora- 
ries, both  in  his  country  and  ours,  an  example  of  high- 
minded  devotion. 

I  was  quite  aware,  in  a  general  way,  that  labors  like 
those  now  for  the  first  time  made  public  had  been  con- 
ducted in  the  United  States,  and  this  knowledge  was  not 
without  influence  upon  my  conduct.  The  first  instru- 
ments mounted  at  the  South  Foreland  were  of  English 
manufacture;  and  I,  on  various  accounts,  entertained  a 
strong  sympathy  for  their  able  constructor,  Mr.  Holmes. 
From  the  outset,  however,  I  resolved  to  suppress  such 
feelings,  as  well  as  all  other  extraneous  considerations, 
individual  or  national;  and  to  aim  at  obtaining  the  best 
instruments,  irrespective  of  the  country  which  produced 
them.  In  reporting,  accordingly,  on  the  observations  of 
May  19  and  20,  1873  (our  first  two  days  at  the  South 
Foreland),  these  were  my  words  to  the  Elder  Brethren  of 
the  Trinity  House: 


PREFACE.  13 

"  In  view  of  the  reported  performance  of  horns  and 
whistles  in  other  places,  the  question  arises  whether  those 
mounted  at  the  South  Foreland,  and  to  which  the  fore- 
going remarks  refer,  are  of  the  best  possible  description. 
...  I  think  our  first  duty  is  to  make  ourselves  acquainted 
with  the  best  instruments  hitherto  made,  no  matter  where 
made;  and  then,  if  home  genius  can  transcend  them,  to 
give  it  all  encouragement.  Great  and  unnecessary  expense 
may  be  incurred,  through  our  not  availing  ourselves  of  the 
results  of  existing  experience. 

"  I  have  always  sympathized,  and  I  shall  always  sym- 
pathize, with  the  desire  of  the  Elder  Brethren  to  encourage 
the  inventor  who  first  made  the  magneto-electric  light 
available  for  lighthouse  purposes.  I  regard  his  aid  and 
counsel  as,  in  many  respects,  invaluable  to  the  corporation. 
But,  however  original  he  may  be,  our  duty  is  to  demand 
that  his  genius  shall  be  expended  in  making  advances  on 
that  which  has  been  already  achieved  elsewhere.  If  the 
whistles  and  horns  that  we  heard  on  the  19th  and  20th  be 
the  very  best  hitherto  constructed,  my  views  have  been 
already  complied  with;  but  if  they  be  not — and  I  am 
strongly  inclined  to  think  that  they  are  not — then  I  would 
submit  that  it  behoves  us  to  have  the  best,  and  to  aim  at 
making  the  South  Foreland,  both  as  regards  light  and 
sound,  a  station  not  excelled  by  any  other  in  the  world." 

On  this  score  it  gives  me  pleasure  to  say  that  I  never 
had  a  difficulty  with  the  Elder  Brethren.  They  agreed 
with  me;  and  two  powerful  steam-whistles,  the  one  from 
Canada,  the  other  from  the  United  States,  together  with 
a  steam-siren — also  an  American  instrument — were  in  due 


u 


PREFACE. 


time  mounted  at  the  South  Foreland.  It  will  be  seen  in 
Chapter  VII.  that  my  strongest  recommendation  applies 
to  an  instrument  for  which  we  are  indebted  to  the  United 
States. 

In  presence  of  these  facts,  it  will  hardly  be  assumed 
that  I  wish  to  withhold  from  the  Lighthouse  Board  of 
Washington  any  credit  that  they  may  fairly  claim.  My 
desire  is  to  be  strictly  just;  and  this  desire  compels  me 
to  express  the  opinion  that  their  Keport  fails  to  estab- 
lish the  inordinate  claim  made  in  its  first  paragraph. 
It  contains  observations,  but  contradictory  observations; 
while  as  regards  the  establishment  of  any  principle  which 
should  reconcile  the  conflicting  results,  it  leaves  our  con- 
dition unimproved. 

But  I  willingly  turn  aside  from  the  discussion  of 
"  claims  "  to  the  discussion  of  science.  Inserted,  as  a  kind 
of  intrusive  element,  into  the  Keport  of  Prof.  Henry, 
is  a  second  Report  by  General  Duane,  founded  on  an  ex- 
tensive series  of  observations  made  by  him  in  1870  and 
1871.  After  stating  with  distinctness  the  points  requir- 
ing decision,  the  general  makes  the  following  remarks: 

"  Before  giving  the  results  of  these  experiments,  some 
facts  will  be  stated  which  will  explain  the  difficulties  of 
determining  the  power  of  the  fog-signal. 

"  There  are  six  steam  fog-whistles  on  the  coast  of 
Maine:  these  have  been  frequently  heard  at  a  distance  of 
twenty  miles,  and  as  frequently  cannot  be  heard  at  the  dis- 
tance of  two  miles,  and  this  with  no  perceptible  difference 
in  the  state  of  the  atmosphere. 

"  The  signal  is  often  heard  at  a  great  distance  in  one 


PREFACE.  15 

direction,  while  in  another  it  will  be  scarcely  audible  at 
the  distance  of  a  mile.  This  is  not  the  effect  of  wind,  as 
the  signal  is  frequently  heard  much  farther  against  the 
wind  than  with  it.1  For  example,  the  whistle  on  Cape 
Elizabeth  can  always  be  distinctly  heard  in  Portland,  a 
distance  of  nine  miles,  during  a  heavy  northeast  snow- 
storm, the  wind  blowing  a  gale  directly  from  Portland 
toward  the  whistle.2 

"  The  most  perplexing  difficulties,  however,  arise  from 
the  fact  that  the  signal  often  appears  to  be  surrounded  by 
a  belt,  varying  in  radius  from  one  to  one  and  a  half  mile, 
from  which  the  sound  appears  to  be  entirely  absent.  Thus, 
in  moving  directly  from  a  station  the  sound  is  audible  for 
the  distance  of  a  mile,  is  then  lost  for  about  the  same  dis- 
tance, after  which  it  is  again  distinctly  heard  for  a  long 
time.  This  action  is  common  to  all  ear-signals,  and  has 
been  at  times  observed  at  all  the  stations,  at  one  of  which 
the  signal  is  situated  on  a  bare  rock  twenty  miles  from 
the  mainland,  with  no  surrounding  objects  to  affect  the 
sound." 

It  is  not  necessary  to  assume  here  the  existence  of  a 
"  belt,"  at  some  distance  from  the  station.  The  passage 
of  an  acoustic  cloud  over  the  station  itself  would  produce 
the  observed  phenomenon. 

Passing  over  the  record  of  many  other  valuable  obser- 

1  That  is  to  say,  homogeneous  air  with  an  opposing  wind,  is  frequently 
more  favorable  to  sound  than  non-homogeneous  air  with  a  favoring 
wind.  "We  made  the  same  experience  at  the  South  Foreland. — J.  T. 

9  Had  this  observation  been  published,  it  could  only  have  given  me 
pleasure  to  refer  to  it  in  my  recent  writings.  It  is  a  striking  confirma- 
tion of  my  observations  on  the  Mer  de  Glace  in  1859. 


16  PREFACE. 

vations,  in  the  Report  of  General  Duane,  I  come  to  a  few 
very  important  remarks  which,  have  a  direct  bearing  upon 
the  present  question : 

"  From  an  attentive  observation,"  writes  the  general, 
"  during  three  years,  of  the  fog-signals  on  this  coast,  and 
from  the  reports  received  from  the  captains  and  pilots  of 
coasting  vessels,  I  am  convinced  that,  in  some  conditions 
of  the  atmosphere,  the  most  powerful  signals  will  be  at 
times  unreliable.1 

"  Now  it  frequently  occurs  that  a  signal  which,  under 
ordinary  circumstances,  would  be  audible  at  the  distance  of 
fifteen  miles,  cannot  be  heard  from  a  vessel  at  the  dis- 
tance of  a  single  mile.  This  is  probably  due  to  the  reflec- 
tion mentioned  by  Humboldt. 

"  The  temperature  of  the  air  over  the  land  where  the 
fog-signal  is  located  being  very  different  from  that  over 
the  sea,  the  sound,  in  passing  from  the  former  to  the  latter, 
undergoes  reflection  at  their  surface  of  contact.  The  cor- 
rectness of  this  view  is  rendered  more  probable  by  the 
fact  that,  when  the  sound  is  thus  impeded  in  the  direction 
of  the  sea,  it  has  been  observed  to  be  much  stronger  in- 
land. 

"  Experiments  and  observation  lead  to  the  conclusion 
that  these  anomalies  in  the  penetration  and  direction  of 
sound  from  fog-signals  are  to  be  attributed  mainly  to  the 
want  of  uniformity  in  the  surrounding  atmosphere,  and 
that  snow,  rain,  and  fog,  and  the  direction  of  the  wind, 

1  Had  I  been  aware  of  its  existence  I  mi^ht  have  used  the  language 
of  General  Duane  to  express  ray  views  on  the  point  here  adverted  to. 
See  Chap.  VII.,  pp.  319-320. 


PREFACE.  IT 

have  much  less  influence  than  has  been  generally  sup- 


The  Eeport  of  General  Duane  is  marked  throughout 
by  fidelity  to  facts,  rare  sagacity,  and  soberness  of  specu- 
lation. The  last  three  of  the  paragraphs  just  quoted, 
exhibit,  in  my  opinion,  the  only  approach  to  a  true  expla- 
nation of  the  phenomena  which  the  Washington  Report 
reveals.  At  this  point,  however,  the  eminent  Chairman 
of  the  Lighthouse  Board  strikes  in  with  the  following 
criticism : 

"  In  the  foregoing  I  differ  entirely  in  opinion  from 
General  Duane,  as  to  the  cause  of  extinction  of  powerful 
sounds  being  due  to  the  unequal  density  of  the  atmos- 
phere. The  velocity  of  sound  is  not  at  all  affected  by 
barometric  pressure;  but  if  the  difference  in  pressure  is 
caused  by  a  difference  in  heat,  or  by  the  expansive  power 
of  vapor  mingled  with  the  air,  a  slight  degree  of  obstruc- 
tion of  sound  may  be  observed.  But  this  effect  we  think 
is  entirely  too  minute  to  produce  the  results  noted  by 
General  Duane  and  Dr.  Tyndall,  while  we  shall  find  in  the 
action  of  currents  above  and  below  a  true  and  efficient 
cause." 

I  have  already  cited  the  remarkable  observation  of 
General  Duane,  that  with  a  snow-storm  from  the  north- 
east blowing  against  the  sound,  the  signal  at  Cape  Eliza- 
beth is  always  heard  at  Portland,  a  distance  of  nine  miles. 
The  observations  at  the  South  Foreland,  where  the  sound 
has  been  proved  to  reach  a  distance  of  more  than  twelve 
miles  against  the  wind,  backed  by  decisive  experiments, 
reduce  to  certainty  the  surmises  of  General  Duane.  It 


13  PREFACE. 

has,  for  example,  been  proved  that  a  couple  of  gas-flames 
placed  in  a  chamber  can,  in  a  minute  or  two,  render  its 
air  so  non-homogeneous  as  to  cut  a  sound  practically  off; 
while  the  same  sound  passes  without  sensible  impediment 
through  showers  of  paper-scraps,  seeds,  bran,  rain-drops, 
and  through  fumes  and  fogs  of  the  densest  description. 
The  sound  also  passes  through  thick  layers  of  calico,  silk, 
serge,  flannel,  baize,  close  felt,  and  through  pads  of  cotton- 
net  impervious  to  the  strongest  light. 

As  long,  indeed,  as  the  air  on  which  snow,  hail,  rain, 
or  fog  is  suspended  is  homogeneous,  so  long  will  sound 
pass  through  the  air,  sensibly  heedless  of  the  suspended 
matter.1  This  point  is  illustrated  upon  a  large  scale  by 
my  own  observations  on  the  Mer  de  Glace,  and  by  those 
of  General  Duane,  at  Portland,  which  prove  the  snow- 
laden  air  from  the  northeast  to  be  a  highly  homogeneous 
medium.  Prof.  Henry  thus  accounts  for  the  fact  that 
the  northeast  snow-wind  renders  the  sound  of  Cape  Eliza- 
beth audible  at  Portland:  In  the  higher  regions  of  the 
atmosphere  he  places  an  ideal  wind,  blowing  in  a  direc- 
tion opposed  to  the  real  one,  which  always  accompanies 
the  latter,  and  which  more  than  neutralizes  its  action.  In 
speculating  thus  he  bases  himself  on  the  reasoning  of 
Prof.  Stokes,  according  to  which  a  sound-wave  moving 
against  the  wind  is  tilted  upward.  The  upper,  and  op- 
posing wind,  is  invented  for  the  purpose  of  tilting  again 
the  already  lifted  sound-wave  downward.  Prof.  Henry 
does  not  explain  how  the  sound-wave  recrosses  the  hos- 

1  This  does  not  peem  more  surprising  than  the  passage  of  light,  or 
radiant  heat,  through  rock-salt. 


PREFACE.  19 

tile  low  current,  nor  does  he  give  any  definite  notion  of 
the  conditions  under  which  it  can  be  shown  that  it  will 
reach  the  observer. 

This,  so  far  as  I  know,  is  the  only  theoretic  gleam 
cast  by  the  Washington  Report  on  the  conflicting  results 
which  have  hitherto  rendered  experiments  on  fog-signals 
so  bewildering.  I  fear  it  is  an  ignis  fatuus,  instead  of  a 
safe  guiding  light.  Prof.  Henry,  however,  boldly  applies 
the  hypothesis  in  a  variety  of  instances.  But  he  dwells 
with  particular  emphasis  upon  a  case  of  non-reciprocity 
which  he  considers  absolutely  fatal  to  my  views  regarding 
the  flocculence  of  the  atmosphere.  The  observation  was 
made  on  board  the  steamer  City  of  Richmond,  during  a 
thick  fog  in  a  night  of  1872.  "  The  vessel  was  approach- 
ing Whitehead  from  the  southwestward,  when,  at  a  dis- 
tance of  about  six  miles  from  the  station,  the  fog-signal, 
which  is  a  10-inch  steam-whistle,  was  distinctly  perceived, 
and  continued  to  be  heard  with  increasing  intensity  of 
sound  until  within  about  three  miles,  when  the  sound  sud- 
denly ceased  to  be  heard,  and  was  not  perceived  again 
until  the  vessel  approached  within  a  quarter  of  a  mile  of 
the  station,  although  from  conclusive  evidence,  furnished 
by  the  keeper,  it  was  shown  that  the  signal  had  been  sound- 
ing during  the  whole  time." 

But  while  the  10-inch  shore-signal  thus  failed  to  make 
itself  heard  at  sea,  a  6-inch  whistle  on  board  the  steamer 
made  itself  heard  on  shore.  Prof.  Henry  thus  turns  this 
fact  against  me.  "  It  is  evident,"  he  writes,  "  that  this 
result  could  not  be  due  to  any  mottled  condition  or  want 
of  acoustic  transparency  in  the  atmosphere,  since  this 


20  PREFACE. 

would  absorb  the  sound  equally  in  both  directions."  Had 
the  observation  been  made  in  a  still  atmosphere,  this  argu- 
ment would,  at  one  time,  have  had  great  force.  But  the 
atmosphere  was  not  still,  and  a  sufficient  reason  for  the 
observed  non-reciprocity  is  to  be  found  in  the  recorded 
fact  that  the  wind  was  blowing  against  the  shore-signal, 
and  in  favor  of  the  ship-signal. 

But  the  argument  of  Prof.  Henry,  on  which  he  places 
his  main  reliance,  would  be  untenable,  even  had  the  air 
been  still.  By  the  very  aerial  reflection  which  he  prac- 
tically ignores,  reciprocity  may  be  destroyed  in  a  calm 
atmosphere.  In  proof  of  this  assertion  I  would  refer  him 
to  a  short  paper  on  "  Acoustic  Reversibility,"  printed  at 
the  end  of  this  volume.1  The  most  remarkable  case  of 
non-reciprocity  on  record,  and  which,  prior  to  the  demon- 
stration of  the  existence  and  power  of  acoustic  clouds, 
remained  an  insoluble  enigma,  is  there  shown  to  be  capable 
of  satisfactory  solution.  These  clouds  explain  perfectly 
the  "  abnormal  phenomena  "  of  Prof.  Henry.  Aware  of 
their  existence,  the  falling  off  and  subsequent  recovery  of 
a  signal-sound,  as  noticed  by  him  and  General  Duane,  is 
no  more  a  mystery,  than  the  interception  of  the  solar  light 
by  a  common  cloud,  and  its  restoration  after  the  cloud  has 
moved  or  melted  away. 

The  clue  to  all  the  difficulties  and  anomalies  of  this 
question  is  to  be  found  in  the  aerial  echoes,  the  significance 
of  which  has  been  overlooked  by  General  Duane,  and  mis- 
interpreted by  Prof.  Henry.  And  here  a  word  might  be 

1  Also  "Proceedings  of  the  Royal  Society,"  vol.  xxiii.,  p.  159,  and 
"  Proceedings  of  the  Royal  Institution,"  vol.  vii.,  p.  344. 


PREFACE.  21 

said  with  regard  to  the  injurious  influence  still  exercised 
by  authority  in  science.  The  affirmations  of  the  highest 
authorities,  that  from  clear  air  no  sensible  echo  ever  comes, 
were  so  distinct,  that  my  mind  for  a  time  refused  to  enter- 
tain the  idea.  Authority  caused  me  for  weeks  to  depart 
from  the  truth,  and  to  seek  counsel  among  delusions.  On 
the  day  our  observations  at  the  South  Foreland  began,  I 
heard  the  echoes.  They  perplexed  me.  I  heard  them 
again  and  again,  and  listened  to  the  explanations  offered 
by  some  ingenious  persons  at  the  Foreland.  They  were 
an  "  ocean-echo :  "  this  is  the  very  phraseology  now  used 
by  Prof.  Henry.  They  were  echoes  "  from  the  crests  and 
slopes  of  the  waves:  "  these  are  the  words  of  the  hypoth- 
esis which  he  now  espouses.  Through  a  portion  of  the 
month  of  May,  through  the  whole  of  June,  and  through 
nearly  the  whole  of  July,  1873,  I  was  occupied  with  these 
echoes;  one  of  the  phases  of  thought  then  passed  through, 
one  of  the  solutions  then  weighed  in  the  balance  and  found 
wanting,  being  identical  with  that  which  Prof.  Henry  now 
offers  for  acceptation. 

But  though  it  thus  deflected  me  from  the  proper  track, 
shall  I  say  that  authority  in  science  is  injurious?  Not 
without  some  qualification.  It  is  not  only  injurious,  but 
deadly,  when  it  cows  the  intellect  into  fear  of  questioning 
it.  But  the  authority  which  so  merits  our  respect  as  to 
compel  us  to  test  and  overthrow  all  its  supports,  before 
accepting  a  conclusion  opposed  to  it,  is  not  wholly  noxious. 
On  the  contrary,  the  disciplines  it  imposes  may  be  in  the 
highest  degree  salutary,  though  they  may  end,  as  in  the 
present  case,  in  the  ruin  of  authority.  The  truth  thus 


22  PREFACE. 

established  is  rendered  firmer  by  our  struggles  to  reach 
it.  I  groped  day  after  day,  carrying  this  problem  of  aerial 
echoes  in  my  mind;  to  the  weariness,  I  fear,  of  some  of 
my  colleagues  who  did  not  know  my  object.  The  ships 
and  boats  afloat,  the  "  slopes  and  crests  of  the  waves,"  the 
visible  clouds,  the  cliffs,  the  adjacent  lighthouses,  the  ob- 
jects landward,  were  all  in  turn  taken  into  account,  and 
all  in  turn  rejected. 

With  regard  to  the  particular  notion  which  now  finds 
favor  with  Prof.  Henry,  it  suggests  the  thought  that  his 
observations,  notwithstanding  their  apparent  variety  and 
extent,  were  really  limited  as  regards  the  weather.  For 
did  they,  like  ours,  embrace  weather  of  all  kinds,  it  is  not 
likely  that  he  would  have  ascribed  to  the  sea-waves  an 
action  which  often  reaches  its  maximum  intensity  when 
waves  are  entirely  absent.  I  will  not  multiply  instances, 
but  confine  myself  to  the  definite  statement  that  the 
echoes  have  often  manifested  an  astonishing  strength 
when  the  sea  was  of  glassy  smoothness.  On  days  when 
the  echoes  were  powerful,  I  have  seen  the  southern  cu- 
muli mirrored  in  the  waveless  ocean,  in  forms  almost  as 
definite  as  the  clouds  themselves.  By  no  possible  appli- 
cation of  the  law  of  incidence  and  reflection  could  the 
echoes  from  such  a  sea  return  to  the  shore;  and  if  we  ac- 
cept for  a  moment  a  statement  which  Prof.  Henry  seems 
to  indorse,  that  sound-waves  of  great  intensity,  when  they 
impinge  upon  a  solid  or  liquid  surface,  do  not  obey  the 
law  of  incidence  and  reflection,  but  "  roll  along  the  surface 
like  a  cloud  of  smoke,"  it  only  increases  the  difficulty. 
Such  a  "  cloud,"  instead  of  returning  to  the  coast  of  Eng- 


PREFACE.  23 

land,  would,  in  our  case,  have  rolled  toward  the  coast  of 
France.  Kothing  that  I  could  say  in  addition  could 
strengthen  the  case  here  presented.  I  will  only  add  one 
further  remark.  When  the  sun  shines  uniformly  on  a 
smooth  sea,  thus  producing  a  practically  uniform  distribu- 
tion of  the  aerial  currents  to  which  the  echoes  are  due,  the 
direction  in  which  the  trumpet-echoes  reach  the  shore  is 
always  that  in  which  the  axis  of  the  instrument  is  pointed. 
At  Dungeness  this  was  proved  to  be  the  case  through- 
out an  arc  of  210° — an  impossible  result,  if  the  direc- 
tion of  reflection  were  determined  by ,  that  of  the  ocean 
waves. 

Rightly  interpreted  and  followed  out,  these  aerial 
echoes  lead  to  a  solution  which  penetrates  and  reconciles 
the  phenomena  from  beginning  to  end.  On  this  point  I 
would  stake  the  issue  of  the  whole  inquiry,  and  to  this 
point  I  would, 'with  special  earnestness,  direct  the  attention 
of  the  Lighthouse  Board  of  Washington.  Let  them  pro- 
long their  observations  into  calm  weather:  if  their  at- 
mosphere resembles  ours — which  I  cannot  doubt — then  I 
affirm  that  they  will  infallibly  find  the  echoes  strong  on 
days  when  all  thought  of  reflection  "  from  the  crests  and 
slopes  of  the  waves  "  must  be  discarded.  The  echoes  afford 
the  easiest  access  to  the  core  of  this  question,  and  it  is  for 
this  reason  that  I  dwell  upon  them  thus  emphatically.  It 
requires  no  refined  skill  or  profound  knowledge  to  master 
the  conditions  of  their  production;  and  these  once  mas- 
tered, the  Lighthouse  Board  of  Washington  will  find  them- 
selves in  the  real  current  of  the  phenomena,  outside  of 
which — I  say  it  with  respect — they  are  now  vainly  specu- 


24  PREFACE. 

lating.  The  acoustic  deportment  of  the  atmosphere  in 
haze,  fog,  sleet,  snow,  rain,  and  hail,  will  be  no  longer  a 
mystery:  even  those  "abnormal  phenomena"  which  are 
now  referred  to  an  imaginary  cause,  or  reserved  for  future 
investigation,  will  be  found  to  fall  naturally  into  place,  as 
illustrations  of  a  principle  as  simple  as  it  is  universal. 


"  With  the  instruments  now  at  our  disposal,  wisely 
established  along  our  coasts,  I  venture  to  think  that  the 
saving  of  property,  in  ten  years,  will  be  an  exceedingly 
large  multiple  of  the  outlay  necessary  for  the  establish- 
ment of  such  signals.  The  saving  of  life  appeals  to  the 
higher  motives  of  humanity."  Such  were  the  words  with 
which  I  wound  up  my  Report  on  Fog-signals.1  One  year 
after  their  utterance,  the  Schiller  goes  to  pieces  on  the 
Scilly  rocks.  A  single  calamity  covers  the  predicted  mul- 
tiple, while  the  sea  receives  three  hundred  and  thirty-three 
victims.  As  regards  the  establishment  of  fog-signals, 
energy  has  been  hitherto  paralyzed  by  their  reputed  un- 
certainty. We  now  know  both  the  reason  and  the  range 
of  their  variations;  and  such  knowledge  places  it  within 
our  power  to  prevent  disasters  like  the  recent  one.  The 
inefficiency  of  bells,  which  caused  their  exclusion  from 
our  inquiry,  was  sadly  illustrated  in  the  case  of  the 
Schiller. 

JOHN  TYNDALL. 

ROYAL  INSTITUTION,  June,  1875. 

1  See  page  348  of  this  volume. 


PREFACE 


THE  FIRST  EDITION. 


IN  the  following  pages  I  have  tried  to  render  the  science 
of  Acoustics  interesting  to  all  intelligent  persons,  including 
those  who  do  not  possess  any  special  scientific  culture. 

The  subject  is  treated  experimentally  throughout,  and 
I  have  endeavored  so  to  place  each  experiment  before  the 
reader,  that  he  should  realize  it  as  an  actual  operation. 
My  desire,  indeed,  has  been  to  give  distinct  images  of  the 
various  phenomena  of  acoustics,  and  to  cause  them  to  be 
seen  mentally  in  their  true  relations. 

I  have  been  indebted  to  the  kindness  of  some  of  my 
English  friends  for  a  more  or  less  complete  examination 
of  the  proof-sheets  of  this  work.  To  my  celebrated  Ger- 
man friend  Clausius,  who  has  given  himself  the  trouble  of 
reading  the  proofs  from  beginning  to  end,  my  especial 
thanks  are  due  and  tendered. 

There  is  a  growing  desire  for  scientific  culture  through- 
out the  civilized  world.  The  feeling  is  natural,  and, 
under  the  circumstances,  inevitable.  For  a  power  which 
influences  so  mightily  the  intellectual  and  material  action 
of  the  age,  could  not  fail  to  arrest  attention  and  challenge 

examination.     In  our  schools  and  universities  a  movement 
25 


26  PREFACE. 

in  favor  of  science  has  begun  which,  no  doubt,  will  end 
in  the  recognition  of  its  claims,  both  as  a  source  of  knowl- 
edge and  as  a  means  of  discipline.  If  by  showing,  how- 
ever inadequately,  the  methods  and  results  of  physical 
science  to  men  of  influence,  who  derive  their  culture  from 
another  source,  this  book  should  indirectly  aid  in  pro- 
moting the  movement  referred  to,  it  will  not  have  been 
written  in  vain. 


CONTENTS. 


CHAPTER  I. 

The  Nerves  and  Sensation.— Production  and  Propagation  of  Sonorous 
Motion. — Experiments  on  Sounding  Bodies  placed  in  Vacuo. — 
Deadening  of  Sound  by  Hydrogen. — Action  of  Hydrogen  on  the 
Voice.— Propagation  of  Sound  through  Air  of  Varying  Density. — 
Reflection  of  Sound.— Echoes. — Refraction  of  Sound.— Diffraction 
of  Sound ;  Case  of  Erith  Village  and  Church. — Influence  of  Tem- 
perature on  Velocity. — Influence  of  Density  and  Elasticity. — New- 
ton's Calculation  of  Velocity. — Thermal  Changes  produced  by  the 
Sonorous  Wave. — Laplace's  Correction  of  Newton's  Formula. — Ra- 
tio of  Specific  Heats  at  Constant  Pressure  and  at  Constant  Volume 
deduced  from  Velocities  of  Sound — Mechanical  Equivalent  of  Heat 
deduced  from  this  Ratio. — Inference  that  Atmospheric  Air  possesses 
no  Sensible  Power  to  radiate  Heat. — Velocity  of  Sound  in  Different 
Gases. — Velocity  in  Liquids  and  Solids. — Influence  of  Molecular 
Structure  on  the  Velocity  of  Sound page  31 

SUMMARY  OF  CHAPTER  I 73 

CHAPTER  II. 

Physical  Distinction  between  Noise  and  Music. — A  Musical  Tone  pro- 
duced by  Periodic,  Noise  produced  by  Unperiodic,  Impulses. — 
Production  of  Musical  Sounds  by  Taps.— Production  of  Musical 
Sounds  by  Puffs. — Definition  of  Pitch  in  Music. — Vibrations  of  a 
Tuning-Fork;  their  Graphic  Representation  on  Smoked  Glass. — 
Optical  Expression  of  the  Vibrations  of  a  Tuning-Fork.— Descrip- 
tion of  the  Siren. — Limits  of  the  Ear ;  Highest  and  Deepest  Tones. 
— Rapidity  of  Vibration  determined  by  the  Siren. — Determination 
of  the  Lengths  of  Sonorous  Waves. — Wave-Lengths  of  the  Voice 
in  Man  and  Woman. — Transmission  of  Musical  Sounds  through 
Liquids  and  Solids 77 

SUMMARY  OF  CHAPTER  II 110 

27 


28  CONTENTS. 

CHAPTER  III. 

Vibration  of  Strings. — How  employed  in  Music. — Influence  of  Sound- 
Boards. — Laws  of  Vibrating  Strings. — Combination  of  Direct  and 
Reflected  Pulses. — Stationary  and  Progressive  Waves. — Nodes  and 
Ventral  Segments. — Application  of  Results  to  the  Vibrations  of 
Musical  Strings. — Experiments  of  Melde. — Strings  set  in  Vibration 
by  Tuning-Forks. — Laws  of  Vibration  thus  demonstrated. — Har- 
monic Tones  of  Strings. — Definition  of  Timbre  or  Quality,  of 
Overtones  and  Clang.— Abolition  of  Special  Harmonics.— Condi- 
tions which  affect  the  Intensity  of  the  Harmonic  Tones. — Optical 
Examination  of  the  Vibrations  of  a  Piano- Wire  .  .  page  113 

SUMMARY  OF  CHAPTER  III 152 

CHAPTER  IV. 

Vibrations  of  a  Rod  fixed  at  Both  Ends :  its  Subdivisions  and  Corre- 
sponding Overtones. — Vibrations  of  a  Rod  fixed  at  One  End. — The 
Kaleidophone. — The  Iron  Fiddle  and  Musical  Box. — Vibrations  of 
a  Rod  free  at  Both  Ends. — The  Claque-bois  and  Glass  Harmonica. 
— Vibrations  of  a  Tuning- Fork :  its  Subdivision  and  Overtones. 
— Vibrations  of  Square  Plates. — Chladni's  Discoveries. — Wheat- 
stone's  Analysis  of  the  Vibrations  of  Plates.— Chladni's  Figures. 
— Vibrations  of  Disks  and  Bells.— Experiments  of  Faraday  and 
Strehlke ^ 156 

SUMMARY  OF  CHAPTER  IV .185 


CHAPTER  V. 

Longitudinal  Vibrations  of  a  Wire.— Relative  Velocities  of  Sound  in 
Brass  and  Iron. — Longitudinal  Vibrations  of  Rods  fixed  at  One 
End.— Of  Rods  free  at  Both  Ends.— Divisions  and  Overtones  of 
Rods  vibrating  longitudinally. — Examination  of  Vibrating  Bars  by 
Polarized  Light. — Determination  of  Velocity  of  Sound  in  Solids. — 
Resonance. — Vibrations  of  Stopped  Pipes:  their  Divisions  and 
Overtones. — Relation  of  the  Tones  of  Stopped  Pipes  to  those  of 
Open  Pipes.— Condition  of  Column  of  Air  within  a  Sounding 
Organ-Pipe. — Reeds  and  Reed-Pipes. — The  Voice. — Overtones  of 
the  Vocal  Chords.— The  Vowel  Sounds.— Kundt's  Experiments. — 
New  Methods  of  determining  the  Velocity  of  Sound  .  .  188 

SUMMARY  OF  CHAPTER  V  .  239 


CONTENTS.  29 

CHAPTER  VI. 

Singing  Flames. — Influence  of  the  Tube  surrounding  the  Flame. — In- 
fluence of  Size  of  Flame. — Harmonic  Notes  of  Flumes. — Effect  of 
Unisonant  Notes  on  Singing  Flames.— Action  of  Sound  on  Naked 
Flames. — Experiments  with  Fish-Tail  and  Bat's- Wing  Burners. — 
Experiments  on  Tall  Flames. — Extraordinary  Delicacy  of  Flames 
as  Acoustic  Reagents. — The  Vowel-Flame. — Action  of  Conversa- 
tional Tones  upon  Flames. — Action  of  Musical  Sounds  on  Smoke- 
Jets.— Constitution  of  Water-Jets.— Plateau's  Theory  of  the  Reso- 
lution of  a  Liquid  Vein  into  Drops. — Action  of  Musical  Sounds  on 
Water-Jets. — A  Liquid  Vein  may  compete  in  Point  of  Delicacy 
with  the  Ear page  244 

SUMMARY  OF  CHAPTER  VI 284 

CHAPTER  VII. 

RESEARCHES    ON    THE    ACOUSTIC    TRANSPARENCY   OF   THE   ATMOSPHERE   IN 
RELATION   TO   THE   QUESTION   OF    FOG-SIGNALLING. 

PART   I. 

Introduction. — Instruments  and  Observations. — Contradictory  Results 
from  the  19th  of  May  to  the  1st  of  July  inclusive. — Solution  of 
Contradictions. — Aerial  Reflection  and  its  Causes. — Aerial  Echoes. 
— Acoustic  Clouds. — Experimental  Demonstration  of  Stoppage  of 
Sound  by  Aerial  Reflection 287 

PART  II. 

INVESTIGATION  OF  THE  CAUSES  WHICH  HAVE  HITHERTO  BEEN  SUPPOSED 
EFFECTIVE  IN  PREVENTING  THE  TRANSMISSION  OF  SOUND  THROUGH 
THE  ATMOSPHERE. 

Action  of  Hail  and  Rain. — Action  of  Snow. — Action  of  Fog :  Observa- 
tions in  London. — Experiments  on  Artificial  Fogs. — Observations 
on  Fogs  at  the  South  Foreland.— Action  of  Wind.— Atmospheric 
Selection.— Influence  of  Sound-Shadow  .....  320 

SUMMARY  OF  CHAPTER  VII 351 


CHAPTER  VEIL 

Law  of  Vibratory  Motions  in  Water  and  Air.— Superposition  of  Vibra- 
tions.— Interference  of  Sonorous  Waves. — Destruction  of  Sound  by 
Sound. — Combined  Action  of  Two  Sounds  nearly  in  Unison  with 


30  CONTENTS. 

each  other.— Theory  of  Beats.— Optical  Illustration  of  the  Principle 
of  Interference. — Augmentation  of  Intensity  by  Partial  Extinction 
of  Vibrations. — Resultant  Tones. — Conditions  of  their  Production. 
—Experimental  Illustrations.— Difference-Tones  and  Summation- 
Tones. — Theories  of  Young  and  Helmholtz  .  .  .  page  354 

SUMMARY  OF  CHAPTER   VIII 383 

CHAPTER  IX. 

Combination  of  Musical  Sounds. — The  smaller  the  Two  Numbers  which 
express  the  Ratio  of  their  Rates  of  Vibration,  the  more  perfect  is 
the  Harmony  of  Two  Sounds. — Notions  of  the  Pythagoreans  re- 
garding Musical  Consonance. — Euler's  Theory  of  Consonance. — 
Theory  of  Helmholtz. — Dissonance  due  to  Beats. — Interference  of 
Primary  Tones  and  of  Overtones. — Sympathetic  Vibrations. — 
Mechanism  of  Hearing.— Schultze's  Bristles.— The  Otolites.— Cor- 
ti's  Fibres. — Graphic  Representation  of  Consonance  and  Disso- 
nance.— Musical  Chords. — The  Diatonic  Scale. — Optical  Illustra- 
tion of  Musical  Intervals. — Lissajous's  Figures.— Various  Modes  of 
Illustrating  the  Composition  of  Vibrations  .  .  .  .385 

SUMMARY  OF  CHAPTER  IX.  .  423 


APPENDIX  I. 

ON  THE  INFLUENCE  OF  MUSICAL  SOUNDS  ON  THE  FLAME  OF  A  JET  OF 
COAL-GAS.    BY  JOHN  LE  CONTE,  M.  D.     .  .  427 


APPENDIX  II. 

ON  ACOUSTIC  REVERSIBILITY 432 

INDEX  .  441 


ILLUSTRATIONS. 

FOG-SIREN Frontispiece 

CHLADNI to  face  p.  168 


SOUND. 


CHAPTEK  I. 

The  Nerves  and  Sensation.— Production  and  Propagation  of  Sonorous 
Motion. — Experiments  on  Sounding  Bodies  placed  in  Vacuo. — 
Deadening  of  Sound  by  Hydrogen. — Action  of  Hydrogen  on  the 
Voice.— Propagation  of  Sound  through  Air  of  Varying  Density. — 
Reflection  of  Sound. — Echoes. — Refraction  of  Sound. — Diffraction 
of  Sound ;  Case  of  Erith  Village  and  Church. — Influence  of  Tem- 
perature on  Velocity. — Influence  of  Density  and  Elasticity. — New- 
ton's Calculation  of  Velocity. — Thermal  Changes  produced  by  the 
Sonorous  Wave.— Laplace's  Correction  of  Newton's  Formula.— Ra- 
tio of  Specific  Heats  at  Constant  Pressure  and  at  Constant  Voluma 
deduced  from  Velocities  of  Sound— Mechanical  Equivalent  of  Heat 
deduced  from  this  Ratio.— Inference  that  Atmospheric  Air  possesses 
no  Sensible  Power  to  radiate  Heat. — Velocity  of  Sound  in  Different 
Gases.— Velocity  in  Liquids  and  Solids.— Influence  of  Molecular 
Structure  on  the  Velocity  of  Sound. 

§  1.  Introduction:  Character  of  Sonorous  Motion. 
Experimental  Illustrations. 

THE  various  nerves  of  the  human  body  have  their  ori- 
gin in  the  brain,  which  is  the  seat  of  sensation.  When 
the  finger  is  wounded,  the  sensor  nerves  convey  to  the 
brain  intelligence  of  the  injury,  and  if  these  nerves  be 
severed,  however  serious  the  hurt  may  be,  no  pain  is  ex- 
perienced. We  have  the  strongest  reason  for  believing 
that  what  the  nerves  convey  to  the  brain  is  in  all  cases 
motion.  The  motion  here  meant  is  not,  however,  that  of 
3  31 


32  SOUND. 

the  nerve  as  a  whole,  but  of  its  molecules  or  smallest  par- 
ticles.1 

Different  nerves  are  appropriated  to  the  transmission 
of  different  kinds  of  molecular  motion.  The  nerves  of 
taste,  for  example,  are  not  competent  to  transmit  the 
tremors  of  light,  nor  is  the  optic  nerve  competent  to  trans- 
mit sonorous  vibrations.  For  these  a  special  nerve  is 
necessary,  which  passes  from  the  brain  into  one  of  the 
cavities  of  the  ear,  and  there  divides  into  a  multitude  of 
filaments.  It  is  the  motion  imparted  to  this,  the  auditory 
nerve,  which,  in  the  brain,  is  translated  into  sound. 

Applying  a  flame  to  a  small  collodion  balloon  which 
contains  a  mixture  of  oxygen  and  hydrogen,  the  gases  ex- 
plode, and  every  ear  in  this  room  is  conscious  of  a  shock, 
which  we  name  a  sound.  How  was  this  shock  transmitted 
from  the  balloon  to  our  organs  of  hearing?  Have  the  ex- 
ploding gases  shot  the  air-particles  against  the  auditory 
nerve  as  a  gun  shoots  a  ball  against  a  target?  No  doubt, 
in  the  neighborhood  of  the  balloon,  there  is  to  some  extent 
a  propulsion  of  particles;  but  no  particle  of  air  from  the 
vicinity  of  the  balloon  reached  the  ear  of  any  person  here 
present.  The  process  was  this:  When  the  flame  touched 
the  mixed  gases  they  combined  chemically,  and  their  union 
was  accompanied  by  the  development  of  intense  heat. 
The  heated  air  expanded  suddenly,  forcing  the  surround- 
ing air  violently  away  on  all  sides.  This  motion  of  the 
air  close  to  the  balloon  was  rapidly  imparted  to  that  a 
little  farther  off,  the  air  first  set  in  motion  coming  at  the 
same  time  to  rest.  The  air,  at  a  little  distance,  passed  its 
motion  on  to  the  air  at  a  greater  distance,  and  came  also 
in  its  turn  to  rest.  Thus  each  shell  of  air,  if  I  may  use  the 
term,  surrounding  the  balloon  took  up  the  motion  of  the 

1  The  rapidity  with  which  an  impression  is  transmitted  through  the 
nerves,  as  first  determined  by  Helmholtz,  and  confirmed  by  Du  Bois- 
Reymond,  is  93  feet  a  second. 


PRODUCTION  AND  PROPAGATION  OF  SOUND.   33 

shell  next  preceding,  and  transmitted  it  to  the  next  suc- 
ceeding shell,  the  motion  being  thus  propagated  as  a  pulse 
or  wave  through  the  air. 

The  motion  of  the  pulse  must  not  be  confounded  with 
the  motion  of  the  particles  which  at  any  moment  constitute 
the  pulse.  For  while  the  wave  moves  forward  through 
considerable  distances,  each  particular  particle  of  air  makes 
only  a  small  excursion  to  and  fro. 

The  process  may  be  rudely  represented  by  the  propa- 
gation of  motion  through  a  row  of  glass  balls,  such  as  are 
employed  in  the  game  of  solitaire.  Placing  the  balls 
along  a  groove  thus,  Fig.  1,  each  of  them  touching  its 
neighbor,  and  urging  one  of  them  against  the  end  of  the 


FIG.  1. 


row:  the  motion  thus  imparted  to  the  first  ball  is  delivered 
up  to  the  second,  the  motion  of  the  second  is  delivered  up 
to  the  third,  and  the  motion  of  the  third  is  imparted  to  the 
fourth;  each  ball,  after  having  given  up  its  motion,  re- 
turning itself  to  rest.  The  last  ball  only  of  the  row  flies 
away.  In  a  similar  way  is  sound  conveyed  from  particle 
to  particle  through  the  air.  The  particles  which  fill  the 
cavity  of  the  ear  are  finally  driven  against  the  tympanic 
membrane,  which  is  stretched  across  the  passage  leading 
from  the  external  air  toward  the  brain.  This  membrane, 
which  closes  outwardly  the  "  drum  "  of  the  ear,  is  thrown 
into  vibration,  its  motion  is  transmitted  to  the  ends  of  the 
auditory  nerve,  and  afterward  along  that  nerve  to  the 


34  SOUND. 

brain,  where  the  vibrations  are  transmitted  into  sound. 
How  it  is  that  the  motion  of  the  nervous  matter  can  thus 
excite  the  consciousness  of  sound  is  a  mystery  which  the 
human  mind  cannot  fathom. 

The  propagation  of  sound  may  be  illustrated  by  another 
homely  but  useful  illustration.  I  have  here  five  young 
assistants,  A,  B,  c,  D,  and  E,  Fig.  2,  placed  in  a  row,  one 
behind  the  other,  each  boy's  hands  resting  against  the 
back  of  the  boy  in  front  of  him.  E  is  now  foremost,  and 
A  finishes  the  row  behind.  I  suddenly  push  A,  A  pushes 
B,  and  regains  his  upright  position;  B  pushes  c;  c  pushes 
D;  D  pushes  E;  each  boy,  after  the  transmission  of  the 
push,  becoming  himself  erect.  E,  having  nobody  in  front, 


is  thrown  forward.  Had  he  been  standing  on  the  edge  of 
a  precipice,  he  would  have  fallen  over;  had  he  stood  in 
contact  with  a  window,  he  would  have  broken  the  glass; 
had  he  been  close  to  a  drum-head,  he  would  have  shaken 
the  drum.  We  could  thus  transmit  a  push  through  a  row 
of  a  hundred  boys,  each  particular  boy,  however,  only 
swaying  to  and  fro.  Thus,  also,  we  send  sound  through 
the  air,  and  shake  the  drum  of  a  distant  ear,  while  each 
particular  particle  of  the  air  concerned  in  the  transmission 
of  the  pulse  makes  only  a  small  oscillation. 

But  we  have  not  yet  extracted  from  our  row  of  boys 
all  that  they  can  teach  us.  When  A  is  pushed  he  may  yield 
languidly,  and  thus  tardily  deliver  up  the  motion  to  his 


A  SONOROUS  WAVE.  35 

neighbor  B.  B  may  do  the  same  to  c,  c  to  D,  and  D  to  E. 
In  this  way  the  motion  might  be  transmitted  with  com- 
parative slowness  along  the  line.  But  A,  when  pushed, 
may,  by  a  sharp  muscular  effort  and  sudden  recoil,  deliver 
up  promptly  his  motion  to  B,  and  come  himself  to  rest;  B 
may  do  the  same  to  c,  c  to  D,  and  D  to  E,  the  motion 
being  thus  transmitted  rapidly  along  the  line.  Now 
this  sharp  muscular  effort  and  sudden  recoil  is  anal- 
ogous to  the  elasticity  of  the  air  in  the  case  of  sound. 
In  a  wrave  of  sound,  a  lamina  of  air,  when  urged  against 
its  neighbor  lamina,  delivers  up  its  motion  and  recoils, 
in  virtue  of  the  elastic  force  exerted  between  them;  and 
the  more  rapid  this  delivery  and  recoil,  or  in  other  words 
the  greater  the  elasticity  of  the  air,  the  greater  is  the  velo- 
city of  the  sound.  ~t  =  ~^r^-i- 

A  very  instructive  modewf  illustrating  the  transmis- 
sion of  a  sound-pulse  is  furnished  by  the  apparatus  repre- 
sented in  Fig.  3,  devised  by  my  assistant,  Mr.  Cottrell. 

FIG.  3. 


It  consists  of  a  series  of  wooden  balls  separated  from  each 
other  by  spiral  springs.  On  striking  the  knob  A,  a  rod 
attached  to  it  impinges  upon  the  first  ball  B,  which  trans- 
mits its  motion  to  c,  thence  it  passes  to  E,  and  so  on  through 
the  entire  series.  The  arrival  at  D  is  announced  by  the 
shock  of  the  terminal  ball  against  the  wood,  or,  if  we  wish, 
by  the  ringing  of  a  bell.  Here  the  elasticity  of  the  air  is 
represented  by  that  of  the  springs.  The  pulse  may  be  ren- 
dered slow  enough  to  be  followed  by  the  eye. 

Scientific  education  ought  to  teach  us  to  see  the  in- 
visible as  well  as  the  visible  in  nature,  to  picture  with  the 
vision  of  the  mind  those  operations  which  entirely  elude 


36  SOUND. 

bodily  vision;  to  look  at  the  very  atoms  of  matter  in  mo- 
tion and  at  rest,  and  to  follow  them  forth,  without  ever 
once  losing  sight  of  them,  into  the  world  of  the  senses,  and 
see  them  there  integrating  themselves  in  natural  phenom- 
ena. With  regard  to  the  point  now  under  consideration, 
we  must  endeavor  to  form  a  definite  image  of  a  wave  of 
sound.  We  ought  to  see  mentally  the  air-particles  when 
urged  outward  by  the  explosion  of  our  balloon  crowding 
closely  together;  but  immediately  behind  this  condensa- 
tion we  ought  to  see  the  particles  separated  more  widely 
apart.  We  must,  in  short,  to  be  able  to  seize  the  conception 
that  a  sonorous  wave  consists  of  two  portions,  in  the  one  of 
which  the  air  is  more  dense,  and  in  the  other  of  which 
it  is  less  dense  than  usual.  A  condensation  and  a  rare- 
faction, then,  are  the  two  constituents  of  a  wave  of  sound. 
This  conception  shall  be  rendered  more  complete  in  our 
next  lecture. 

§  2.  Experiments  in  Vacuo,  in  Hydrogen,  and  on  Moun- 
tains. 

That  air  is  thus  necessary  to  the  propagation  of  sound 
was  proved  by  a  celebrated  experiment  made  before  the 
Eoyal  Society,  by  a  philosopher  named  Hawksbee,  in 
1705.1  He  so  fixed  a  bell  within  the  receiver  of  an  air- 
pump  that  he  could  ring  the  bell  when  the  receiver  was  ex- 
hausted. Before  the  air  was  withdrawn  the  sound  of  the 
bell  was  heard  within  the  receiver;  after  the  air  was  with- 
drawn the  sound  became  so  faint  as  to  be  hardly  percepti- 
ble. An  arrangement  is  before  you  which  enables  us  to 
repeat  in  a  very  perfect  manner  the  experiment  of  Hawks- 
bee.  Within  this  jar,  GG',  Fig.  4,  resting  on  the  plate  of 
an  air-pump  is  a  bell,  B,  associated  with  clock-work.2  After 

1  And  long  previously  by  Robert  Boyle. 

3  A  very  effective  instrument,  presented  to  the  Royal  Institution  by 
Mr.  Warren  De  La  Rue. 


BELL  IN  VACUO. 


FIG.  4. 


the  jar  has  been  exhausted  as  perfectly  as  possible,  I  release, 
by  means  of  a  rod,  rr',  which  passes  air-tight  through  the 
top  of  the  vessel,  the  detent  which  holds  the  hammer.  It 
strikes,  and  you  see  it  striking,  but  only  those  close  up  to 
the  bell  can  hear  the  sound.  Hydrogen  gas,  which  you 
know  is  fourteen  times  lighter  than  air,  is  now  allowed  to 
enter  the  vessel.  The  sound  of  the  bell  is  not  augmented 
by  the  presence  of  this  attenuated  gas,  though  the  receiver 
is  now  full  of  it.  By  working  the  pump,  the  atmosphere 
round  the  bell  is  rendered  still 
more  attenuated.  In  this  way 
we  obtain  a  vacuum  more  per- 
fect than  that  of  Hawksbee,  and 
this  is  important,  for  it  is 
the  last  traces  of  air  that  are 
chiefly  effective  in  this  ex- 
periment. You  now  see  the 
hammer  pounding  the  bell,  but 
you  hear  no  sound.  Even 
when  the  ear  is  placed  against 
the  exhausted  receiver,  not 
the  faintest  tinkle  is  heard. 
Observe  also  that  the  bell  is 
suspended  by  strings,  for  if  it 
were  allowed  to  rest  upon  the 
plate  of  the  air-pump,  the 
vibrations  would  be  communi- 
cated to  the  plate,  and  thence 
transmitted  to  the  air  outside. 
Permitting  the  air  to  enter  the  jar  with  as  little  noise  as 
possible,  you  immediately  hear  a  feeble  sound,  which 
grows  louder  as  the  air  becomes  more  dense,  until  finally 
every  person  in  this  large  assembly  distinctly  hears  the 
ringing  of  the  bell.1 

1  By  directing  the  beam  of  an  electric  lamp  on  glass  bulbs  filled 


38  SOUND. 

Sir  John  Leslie  found  hydrogen  singularly  incompe- 
tent to  act 'as  the  vehicle  of  the  sound  of  a  bell  rung  in  the 
gas.  More  than  this,  he  emptied  a  receiver  like  that  be- 
fore you  of  half  its  air,  and  plainly  heard  the  ringing  of 
the  bell.  On  permitting  hydrogen  to  enter  the  half-filled 
receiver  until  it  was  wholly  filled,  the  sound  sank  until  it 
was  scarcely  audible.  This  result  remained  an  enigma 
until  it  received  a  simple  and  satisfactory  explanation  at 
the  hands  of  Prof.  Stokes.  When  a  common  pendulum 
oscillates  it  tends  to  form  a  condensation  in  front  and  a 
rarefaction  behind.  But  it  is  only  a  tendency;  the  mo- 
tion is  so  slow,  and  the  air  is  so  elastic,  that  it  moves  away 
in  front  before  it  is  sensibly  condensed,  and  fills  the  space 
behind  before  it  can  become  sensibly  dilated.  Hence 
waves  or  pulses  are  not  generated  by  the  pendulum.  It 
requires  a  certain  sharpness  of  shock  to  produce  the  con- 
densation and  rarefaction  which  constitute  a  wave  of  sound 
in  air. 

The  more  elastic  and  mobile  the  gas,  the  more  able 
will  it  be  to  move  away  in  front  and  to  fill  the  space  be- 
hind, and  thus  to  oppose  the  formation  of  rarefactions 
and  condensations  by  a  vibrating  body.  Now  hydrogen  is 
much  more  mobile  than  air;  and  hence  the  production  of 
sonorous  waves  in  it  is  attended  with  greater  difficulty 
than  in  air.  A  rate  of  vibration  quite  competent  to  pro- 
duce sound-waves  in  the  one  may  be  wholly  incompetent 
to  produce  them  in  the  other.  Both  calculation  and  obser- 
vation prove  the  correctness  of  this  explanation,  to  which 
we  shall  again  refer. 

At  great  elevations  in  the  atmosphere  sound  is  sensibly 
diminished  in  loudness.  De  Saussure  thought  the  explo- 
sion of  a  pistol  at  the  summit  of  Mont  Blanc  to  be  about 

with  a  mixture  of  eqnal  volumes  of  chlorine  and  hvdrogen,  I  hare 
caused  the  bulbs  to  explode  in  vacuo  and  in  air.  The  difference,  though 
not  so  striking  as  I  at  first  expected,  was  perfectly  distinct. 


EFFECT  OF  HYDROGEN  UPON  THE  VOICE.          39 

equal  to  that  of  a  common  cracker  below.  I  have  several 
times  repeated  this  experiment;  first,  in  default  of  any- 
thing better,  with  a  little  tin  cannon,  the  torn  remnants  of 
which  are  now  before  you,  and  afterward  with  pistols. 
What  struck  me  was  the  absence  of  that  density  and  sharp- 
ness in  the  sound  which  characterize  it  at  lower  elevations. 
The  pistol-shot  resembled  the  explosion  of  a  champagne 
bottle,  but  it  was  still  loud.  The  withdrawal  of  half  an 
atmosphere  does  not  very  materially  affect  our  ringing 
bell,  and  air  of  the  density  found  at  the  top  of  Mont  Blanc 
is  still  capable  of  powerfully  affecting  the  auditory  nerve. 
That  highly  attenuated  air  is  able  to  convey  sound  of 
great  intensity  is  forcibly  illustrated  by  the  explosion  of 
meteorites  at  elevations  where  the  tenuity  of  the  atmos- 
phere must  be  almost  infinite.  Here,  however,  the  initial 
disturbance  must  be  exceedingly  great. 

The  motion  of  sound,  like  all  other  motion,  is  enfeebled 
by  its  transference  from  a  light  body  to  a  heavy  one. 
When  the  receiver  which  has  hitherto  covered  our  bell  is 
removed,  you  hear  how  much  more  loudly  it  rings  in  the 
open  air.  When  the  bell  was  covered  the  aerial  vibra- 
tions were  first  communicated  to  the  heavy  glass  jar,  and 
afterward  by  the  jar  to  the  air  outside;  a  great  diminution 
of  intensity  being  the  consequence.  The  action  of  hydro- 
gen gas  upon  the  voice  is  an  illustration  of  the  same  kind. 
The  voice  is  formed  by  urging  air  from  the  lungs  through 
an  organ  called  the  larynx,  where  it  is  thrown  into  vibra- 
tion by  the  vocal  cords  which  thus  generate  sound.  But 
when  the  lungs  are  filled  with  hydrogen,  the  vocal  cords 
on  speaking  produce  a  vibratory  motion  in  the  hydrogen, 
which  then  transfers  the  motion  to  the  outer  air.  By 
this  transference  from  a  light  gas  to  a  heavy  one  the  voice 
is  so  weakened  as  to  become  a  mere  squeak.1 

1  It  may  be  that  the  gas  fails  to  throw  the  vocal  chords  into  suffi- 
ciently strong  vibration.     The  laryngoscope  might  decide  this  question. 


40  SOUND. 

The  intensity  of  a  sound  depends  on  the  density  of  the 
air  in  which  the  sound  is  generated,  and  not  on  that  of  the 
air  in  which  it  is  heard.1  Supposing  the  summit  of  Mont 
Blanc  to  be  equally  distant  from  the  top  of  the  Aiguille 
Verte  and  the  bridge  at  Chamouni;  and  supposing  two 
observers  stationed,  the  one  upon  the  bridge  and  the  other 
upon  the  Aiguille:  the  report  of  a  cannon  fired  on  Mont 
Blanc  would  reach  both  observers  with  the  same  intensity, 
though  in  the  one  case  the  sound  would  pursue  its  way 
through  the  rare  air  above,  while  in  the  other  it  would  de- 
scend through  the  denser  air  below.  Again,  let  a  straight 
line  equal  to  that  from  the  bridge  at  Chamouni  to  the 
summit  of  Mont  Blanc  be  measured  along  the  earth's  sur- 
face in  the  valley  of  Chamouni,  and  let  two  observers  be 
stationed,  the  one  on  the  summit  and  the  other  at  the  end 
of  the  line:  the  report  of  a  cannon  fired  on  the  bridge 
would  reach  both  observers  with  the  same  intensity,  though 
in  the  one  case  the  sound  would  be  propagated  through 
the  dense  air  of  the  valley,  and  in  the  other  case  would 
ascend  through  the  rarer  air  of  the  mountain.  Finally, 
charge  two  cannon  equally,  and  fire  one  of  them  at  Cha- 
mouni and  the  other  at  the  top  of  Mont  Blanc:  the  one 
fired  in  the  heavy  air  below  may  be  heard  above,  while  the 
one  fired  in  the  light  air  above  is  unheard  below. 

§  3.  Intensity  of  Sound.     Law  of  Inverse  Squares. 

In  the  case  of  our  exploding  balloon  the  wave  of 
sound  expands  on  all  sides,  the  motion  produced  by  the 
explosion  being  thus  diffused  over  a  continually  augment- 
ing mass  of  air.  It  is  perfectly  manifest  that  this  cannot 
occur  without  an  enfeeblement  of  the  motion.  Take  the 
case  of  a  thin  shell  of  air  with  a  radius  of  one  foot,  reck- 
oned from  the  centre  of  explosion.  A  shell  of  air  of  the 
same  thickness,  but  of  two  feet  radius,  will  contain  four 
1  Poisson.  "  Mecanique,"  vol.  ii.,  p.  707. 


INTENSITY  OF  SOUND.  41 

times  the  quantity  of  matter;  if  its  radius  be  three  feet, 
it  will  contain  nine  times  the  quantity  of  matter;  if  four 
feet,  it  will  contain  sixteen  times  the  quantity  of  matter, 
and  so  on.  Thus  the  quantity  of  matter  set  in  motion 
augments  as  the  square  of  the  distance  from  the  centre 
of  explosion.  The  intensity  or  loudness  of  sound  dimin- 
ishes in  the  same  proportion.  We  express  this  law  by  say- 
ing that  the  intensity  of  the  sound  varies  inversely  as  the  / 
square  of  the  distance. 

Let  us  look  at  the  matter  in  another  light.  The  me- 
chanical effect  of  a  ball  striking  a  target  depends  on  two 
things — the  weight  of  the  ball,  and  the  velocity  with 
which  it  moves.  The  effect  is  proportional  to  the  weight 
simply ;  but  it  is  proportional  to  the  square  of  the  velocity. 
The  proof  of  this  is  easy,  but  it  belongs  to  ordinary  me- 
chanics rather  than  to  our  present  subject.  Now  what  is 
true  of  the  cannon-ball  striking  a  target  is  also  true  of  an 
air-particle  striking  the  tympanum  of  the  ear.  Fix  your 
attention  upon  a  particle  of  air  as  the  sound-wave  passes 
over  it;  it  is  urged  from  its  position  of  rest  toward  a 
neighbor  particle,  first  with  an  accelerated  motion,  and 
then  with  a  retarded  one.  The  force  which  first  urges  it 
is  opposed  by  the  resistance  of  the  air,  which  finally  stops 
the  particle  and  causes  it  to  recoil.  At  a  certain  point  of 
its  excursion  the  velocity  of  the  particle  is  its  maximum. 
The  intensity  of  the  sound  is  proportional  to  the  square  / 
of  this  maximum  velocity. 

The  distance  through  which  the  air-particle  moves  to 
and  fro,  when  the  sound-wave  passes  it,  is  called  the  am- 
plitude of  the  vibration.  The  intensity  of  the  sound  is 
proportional  to  the  square  of  the  amplitude. 

§  4.  Confinement  of  Sound-waves  in  Tubes. 

This  weakening  of  the  sound,  according  to  the  law  of 
inverse  squares,  would  not  take  place  if  the  sound-wave 


42  SOUND. 

were  so  confined  as  to  prevent  its  lateral  diffusion.  By 
sending  it  through  a  tube  with  a  smooth  interior  surface 
we  accomplish  this,  and  the  wave  thus  confined  may  be 
transmitted  to  great  distances  with  very  little  diminution 
of  intensity.  Into  one  end  of  this  tin  tube,  fifteen  feet 
long,  I  whisper  in  a  manner  quite  inaudible  to  the  people 
nearest  to  me,  but  a  listener  at  the  other  end  hears  me 
distinctly.  If  a  watch  be  placed  at  one  end  of  the  tube, 
a  person  at"  the  other  end  hears  the  ticks,  though  nobody 
else  does.  At  the  distant  end  of  the  tube  is  now  placed  a 
lighted  candle,  c,  Fig  5.  When  the  hands  are  clapped  at 
this  end,  the  flame  instantly  ducks  down  at  the  other. 

FIG.  5.  B<S 

J 


It  is  not  quite  extinguished,  but  it  is  forcibly  depressed. 
When  two  books,  B  B',  Fig.  5,  are  clapped  together,  the 
candle  is  blown  out.1  You  may  here  observe,  in  a  rough 
way,  the  speed  with  which  the  sound-wave  is  propagated. 
The  instant  the  clap  is  heard  the  flame  is  extinguished. 
I  do  not  say  that  the  time  required  by  the  sound  to  travel 
this  tube  is  immeasurably  short,  but  simply  that  the  in- 
terval is  too  short  for  your  senses  to  appreciate  it. 

That  it  is  a  pulse  and  not  a  puff  of  air  is  proved  by 
filling  one  end  of  the  tube  with  the  smoke  of  brown  paper. 
On  clapping  the  books  together  no  trace  of  this  smoke  is 
ejected  from  the  other  end.  The  pulse  has  passed  through 
both  smoke  and  air  without  carrying  either  of  them  along 
with  it. 

1  To  converge  the  pulse  upon  the  flame,  the  tube  was  caused  to  end 
in  a  cone. 


TRANSMISSION  OF  SOUND  THROUGH  TUBES.        43 

An  effective  mode  of  throwing  the  propagation  of  a 
pulse  through  air  has  been  devised  by  my  assistant.  The 
two  ends  of  a  tin  tube  fifteen  feet  long  are  stopped  by 
sheet  India-rubber  stretched  across  them.  At  one  end,  e, 
a  hammer  with  a  spring  handle  rests  against  the  India- 
rubber;  at  the  other  end  is  an  arrangement  for  the  striking 
of  a  bell,  c.  Drawing  back  the  hammer  e  to  a  distance 
measured  on  the  graduated  circle  and  liberating  it,  the 
generated  pulse  is  propagated  through  the  tube,  strikes 
the  other  end,  drives  away  the  cork  termination  a  of  the 

FIG.  6. 


lever  a  &,  and  causes  the  hammer  &  to  strike  the  bell.  The 
rapidity  of  propagation  is  well  illustrated  here.  When 
hydrogen  (sent  through  the  India-rubber  tube  H)  is  substi- 
tuted for  air  the  bell  does  not  ring. 

The  celebrated  French  philosopher,  Biot,  observed  the 
transmission  of  sound  through  the  empty  water-pipes  of 
Paris,  and  found  that  he  could  hold  a  conversation  in  a 
low  voice  through  an  iron  tube  3,120  feet  in  length.  The 
lowest  possible  wrhisper,  indeed,  could  be  heard  at  this  dis- 
tance, while  the  firing  of  a  pistol  into  one  end  of  the  tube 
quenched  a  lighted  candle  at  the  other. 

§  5.  The  Reflection  of  Sound.     Resemblances  to  Light. 

The  action  of  sound  thus  illustrated  is  exactly  the  same 
as  that  of  light  and  radiant  heat.  They,  like  sound,  are 


44  SOUND. 

wave-motions.  Like  sound  they  diffuse  themselves  in 
space,  diminishing  in  intensity  according  to  the  same  law. 
Like  sound  also,  light  and  radiant  heat,  when  sent  through 
a  tube  with  a  reflecting  interior  surface,  may  be  conveyed 
to  great  distances  with  comparatively  little  loss.  In  fact, 
every  experiment  on  the  reflection  of  light  has  its  anal- 
ogy in  the  reflection  of  sound.  On  yonder  gallery  stands 
an  electric  lamp,  placed  close  to  the  clock  of  this  lecture- 
room.  An  assistant  in  the  gallery  ignites  the  lamp,  and 
directs  its  powerful  beam  upon  a  mirror  placed  here  be- 
hind the  lecture-table.  By  the  act  of  reflection  the  diver- 
gent beam  is  converted  into  this  splendid  luminous  cone 
traced  out  upon  the  dust  of  the  room.  The  point  of  con- 
vergence being  marked  and  the  lamp  extinguished,  I  place 
my  ear  at  that  point.  Here  every  sound-wave  sent  forth  by 
the  clock  and  reflected  by  the  mirror  is  gathered  up,  and 
the  ticks  are  heard  as  if  they  came,  not  from  the  clock,  but 
from  the  mirror.  Let  us  stop  the  clock,  and  place  a  watch 
w,  Fig.  7,  at  the  place  occupied  a  moment  ago  by  the  elec- 
FIG.  7. 


trie  light.  At  this  great  distance  the  ticking  of  the  watch 
is  distinctly  heard.  The  hearing  is  much  aided  by  intro- 
ducing the  end  f  of  a  glass  funnel  into  the  ear,  the  fun- 
nel here  acting  the  part  of  an  ear-trumpet.  "We  know, 


REFLECTION  OF  SOUND  BY  MIRRORS.  45 

moreover,  that  in  optics  the  positions  of  a  body  and  of  its 
image  are  reversible.  When  a  candle  is  placed  at  this  lower 
focus,  you  see  its  image  on  the  gallery  above,  and  I  have 
only  to  turn  the  mirror  on  its  stand  to  make  the  image  of 
the  flame  fall  upon  any  one  of  the  row  of  persons  who  oc- 
cupy the  front  seat  in  the  gallery.  Removing  the  candle, 
and  putting  the  watch,  w,  Fig.  8,  in  its  place,  the  person  on 
whom  the  light  fell  distinctly  hears  the  sound.  When 
the  ear  is  assisted  by  the  glass  funnel,  the  reflected  ticks 
of  the  clock  in  our  first  experiment  are  so  powerful  as  to 
suggest  the  idea  of  something  pounding  against  the  tym- 
panum, while  the  direct  ticks  are  scarcely,  if  at  all,  heard. 


FIG.  8. 


One  of  these  two  parabolic  mirrors,  n  ri,  Fig.  9,  is 
placed  upon  the  table,  the  other,  ra  ra',  being  drawn  up  to 
the  ceiling  of  this  theatre;  they  are  five-and-twenty  feet 
apart.  When  the  carbon-points  of  the  electric  light  are 
placed  in  the  focus  a  of  the  lower  mirror  and  ignited,  a  fine 
luminous  cylinder  rises  like  a  pillar  to  the  upper  mirror, 
which  brings  the  parallel  beam  to  a  focus.  At  that  focus 
is  seen  a  spot  of  sunlike  brilliancy,  due  to  the  reflection  of 
the  light  from  the  surface  of  a  watch,  w,  there  suspended. 
The  watch  is  ticking,  but  in  my  present  position  I  do  not 


SOUND. 


FIG.  9. 


hear  it.  At  this  lower  focus,  a,  however,  we  have  the  en- 
ergy of  every  sonorous  wave  converged.  Placing  the  ear 
at  a,  the  ticking  is  as  audible  as  if  the  watch  were  at  hand ; 
the  sound,  as  in  the  former  case,  appearing  to  proceed,  not 
from  the  watch  itself,  but  from  the  lower  mirror.1 

Curved  roofs  and  ceilings  and  bellying  sails  act  as 
mirrors  upon  sound.     In  our  old  laboratory,  for  example, 

the  singing  of  a  kettle 
seemed,  in  certain  po- 
sitions, to  come,  not 
from  the  fire  on  which 
it  was  placed,  but 
from  the  ceiling.  In- 
convenient secrets 
have  been  thus  re- 
vealed, an  instance  of 
which  has  been  cited 
by  Sir  John  Her- 
schel.2  In  one  of 
the  cathedrals  in 
Sicily  the  confes- 
sional was  so  placed 
that  the  whispers  of 
the  penitents  were  re- 
flected by  the  curved 
roof,  and  brought  to 
a  focus  at  a  distant 
part  of  the  edifice. 
The  focus  was  discov- 
ered by  accident,  and  for  some  time  the  person  who  discov- 

1  It  is  recorded  that  a  bell  placed  on  an  eminence  in  Heligoland 
failed,  on  account  of  its  distance,  to  be  heard  in  the  town.  A  parabolic 
reflector  placed  behind  the  bell,  so  as  to  reflect  the  sound-waves  in  the 
direction  of  the  long,  sloping  street,  caused  the  strokes  of  the  bell  to  be 
distinctly  heard  at  all  times.  This  observation  needs  verification. 

*  "  Encyclopaedia  Metropolitana,"  art.  "  Sound." 


ECHOES.  47 

ered  it  took  pleasure  in  hearing,  and  in  bringing  his  friends 
to  hear,  utterances  intended  for  the  priest  alone.  One  day, 
it  is  said,  his  own  wife  occupied  the  penitential  stool,  and 
both  he  and  his  friends  were  thus  made  acquainted  with  se- 
crets which  were  the  reverse  of  amusing  to  one  of  the  party. 

When  a  sufficient  interval  exists  between  a  direct  and 
a  reflected  sound  we  hear  the  latter  as  an  echo. 

Sound,  like  light,  may  be  reflected  several  times  in 
succession,  and,  as  the  reflected  light  under  these  circum- 
stances becomes  gradually  feebler  to  the  eye,  so  the  sus- 
cessive  echoes  become  gradually  feebler  to  the  ear.  In 
mountain-regions  this  repetition  and  decay  of  sound  pro- 
duce wonderful  and  pleasing  effects.  Visitors  to  Killarney 
will  remember  the  fine  echo  in  the  Gap  of  Dunloe.  When 
a  trumpet  is  sounded  in  a  proper  place  in  the  Gap,  the 
sonorous  waves  reach  the  air  in  succession  after  one,  two, 
three,  or  more  reflections  from  the  adjacent  cliffs,  and  thus 
die  away  in  the  sweetest  cadences.  There  is  a  deep  cul-de- 
sac,  called  the  Ochsenthal,  formed  by  the  great  cliffs  of 
the  Engelhb'rner,  near  Rosenlaui,  in  Switzerland,  where 
the  echoes  warble  in  a  wonderful  manner.  The  sound  of 
the  Alpine  horn,  echoed  from  the  rocks  of  the  Wetterhorn 
or  the  Jungfrau,  is  in  the  first  instance  heard  roughly. 
But  by  successive  reflections  the  notes  are  rendered  more 
soft  and  flute-like,  the  gradual  diminution  of  intensity 
giving  the  impression  that  the  source  of  sound  is  retreat- 
ing farther  and  farther  into  the  solitudes  of  ice  and  snow. 
The  repetition  of  echoes  is  also  in  part  due  to  the  fact  that 
the  reflecting  surfaces  are  at  different  distances  from  the 
hearer. 

In  large  unfurnished  rooms  the  mixture  of  direct  and 
reflected  sound  sometimes  produces  very  curious  effects. 
Standing,  for  example,  in  the  gallery  of  the  Bourse  at 
Paris,  you  hear  the  confused  vociferation  of  the  excited 
multitude  below.  You  see  all  the  motions — of  their  lips 
4 


48  SOUND. 

as  well  as  of  their  hands  and  arm.  You  know  they  are 
speaking — often,  indeed,  with  vehemence,  but  what  they 
say  you  know  not.  The  voices  mix  with  their  echoes  into 
a  chaos  of  noise,  out  of  which  no  intelligible  utterance  can 
emerge.  The  echoes  of  a  room  are  materially  damped  by 
its  furniture.  The  presence  of  an  audience  may  also  ren- 
der intelligible  speech  possible  where,  without  an  audience, 
the  definition  of  the  direct  voice  is  destroyed  by  its  echoes. 
On  the  16th  of  May,  1865,  having  to  lecture  in  the  Senate 
House  of  the  University  of  Cambridge,  I  first  made  some 
experiments  as  to  the  loudness  of  voice  necessary  to  fill  the 
room,  and  was  dismayed  to  find  that  a  friend,  placed  at  a 
distant  part  of  the  hall,  could  not  follow  me  because  of  the 
echoes.  The  assembled  audience,  however,  so  quenched 
the  sonorous  waves,  that  the  echoes  were  practically  absent, 
and  my  voice  was  plainly  heard  in  all  parts  of  the  Senate 
House. 

Sounds  are  also  said  to  be  reflected  from  the  clouds. 
Arago  reports  that,  when  the  sky  is  clear,  the  report  of  a 
cannon  on  an  open  plain  is  short  and  sharp,  while  a  cloud 
is  sufficient  to  produce  an  echo  like  the  rolling  of  distant 
thunder.  The  subject  of  aerial  echoes  will  be  subsequent- 
ly treated  at  length,  when  it  will  be  shown  that  Arago's 
conclusion  requires  correction. 

Sir  John  Herschel,  in  his  excellent  article  "  Sound,"  in 
the  "  Encyclopaedia  Metropolitan,"  has  collected  with 
others  the  following  instances  of  echoes.  An  echo  in 
Woodstock  Park  repeats  seventeen  syllables  by  day  and 
twenty  by  night;  one,  on  the  banks  of  the  Lago  del  Lupo, 
above  the  fall  of  Terni,  repeats  fifteen.  The  tick  of  a 
watch  may  be  heard  from  one  end  of  the  abbey  church 
of  St.  Albans  to  the  other.  In  Gloucester  Cathedral,  a 
gallery  of  an  octagonal  form  conveys  a  whisper  seventy- 
five  feet  across  the  nave.  In  the  whispering-gallery  of 
St.  Paul's,  the  faintest  sound  is  conveyed  from  one  side  to 


REFRACTION  OF  SOUND  BY  LENSES.  49 

the  other  of  the  dome,  but  is  not  heard  at  any  inter- 
mediate point.  At  Carisbrook  Castle,  in  the  Isle  of 
Wight,  is  a  well  two  hundred  and  ten  feet  deep  and 
twelve  wide.  The  interior  is  lined  by  smooth  masonry; 
when  a  pin  is  dropped  into  the  well  it  is  distinctly  heard 
to  strike  the  water.  Shouting  or  coughing  into  this  well 
produces  a  resonant  ring  of  some  duration.1 

§  6.  Refraction  of  Sound. 

Another  important  analogy  between  sound  and  light 
has  been  established  by  M.  Sondhauss.2  When  a  large 
lens  is  placed  in  front  of  our  lamp,  the  lens  compels  the 
rays  of  light  that  fall  upon  it  to  deviate  from  their  direct 
and  divergent  course,  and  to  form  a  convergent  cone  be- 
hind it.  This  refraction  of  the  luminous  beam  is  a  con- 
sequence of  the  retardation  suffered  by  the  light  in  passing 

FIG.  10. 


through  the  glass.  Sound  may  be  similarly  refracted  by 
causing  it  to  pass  through  a  lens  which  retards  its  motion. 
Such  a  lens  is  formed  when  we  fill  a  thin  balloon  with 
some  gas  heavier  than  air.  A  collodion  balloon,  B,  Fig. 
10,  filled  with  carbonic-acid  gas,  the  envelope  being  so 

1  Placing  himself  close  to  the  upper  part  of  the  wall  of  the  London 
Colosseum,  a  circular  building  one  hundred  and  thirty  feet  in  diameter, 
Mr.  Wheatstone  found  a  word  pronounced  to  be  repeated  a  great  many 
times.  A  single  exclamation  appeared  like  a  peal  of  laughter,  while  the 
tearing  of  a  piece  of  paper  was  like  the  patter  of  hail. 

2  Poggendor/'s  Annalen,  vol.  Ixxxv.,  p.  378;  Philosophical  Maga- 
zine, vol.  v.,  p.  73. 


50  SOUND. 

thin  as  to  yield  readily  to  the  pulses  which  strike  against 
it,  answers  the  purpose.1  A  watch,  w,  is  hung  up  close  to 
the  lens,  beyond  which,  and  at  a  distance  of  four  or  five 
feet  from  the  lens,  is  placed  the  ear,  assisted  by  the  glass 
funnel  f  /'.  By  moving  the  head  about,  a  position  is 
soon  discovered  in  which  the  ticking  is  particularly  loud. 
This,  in  fact,  is  the  focus  of  the  lens.  If  the  ear  be 
moved  from  this  focus  the  intensity  of  the  sound  falls; 
if,  when  the  ear  is  at  the  focus,  the  balloon  be  removed, 
the  ticks  are  enfeebled;  on  replacing  the  balloon  their 
force  is  restored.  The  lens,  in  fact,  enables  us  to  hear 
the  ticks  distinctly  when  they  are  perfectly  inaudible  to 
the  unaided  ear. 

How  a  sound-wave  is  thus  converged  may  be  compre- 
hended by  reference  to  Fig.  11.     Let  m  o  n  o"  be  a  section 
of  the  sound-lens,  and  aba  portion  of  a  sonorous  wave  ap- 
pIG    jj  preaching  it  from  a  distance. 

cc b       The  middle  point,  o,  of  the 

wave  first  touches  the  lens, 
and  is  first  retarded  by  it. 
By  the  time  the  ends  a  and 
6,  still  moving  through  air, 
reach  the  balloon,  the  middle 
point  o,  pursuing  its  way 
through  the  heavier  gas  with- 
in, will  have  only  reached  o'. 
The  wave  is  therefore  broken  at  o';  and  the  direction  of 
motion  being  at  right  angles  to  the  face  of  the  wave,  the 
two  halves  will  encroach  upon  each  other.  This  conver- 
gence of  the  two  halves  of  the  wave  is  augmented  on  quit- 
ting the  lens.  For  when  o'  has  reached  o",  the  two  ends  a 
and  b  will  have  pushed  forward  to  a  greater  distance,  say 
to  a'  and  b'.  Soon  afterward  the  two  halves  of  the  wave 
will  cross  each  other,  or  in  other  words  come  to  a  focus, 
1  Thin  India-rubber  balloons  also  form  excellent  sound-lenses. 


DIFFRACTION  OF  SOUND— ERITH  EXPLOSION.       51 

the  air  at  ^he  focus  being  agitated  by  the  sum  of  the  mo- 
tions of  the  two  waves.1 

§  7.  Diffraction  of  Sound:  illustrations  offered  by  great 
Explosions. 

"When  a  long  sea-roller  meets  an  isolated  rock  in  its 
passage,  it  rises  against  the  rock  and  embraces  it  all  round. 
Facts  of  this  nature  caused  Newton  to  reject  the  undula- 
tory  theory  of  light.  He  contended  that  if  light  were  a 
product  of  wave-motion  we  could  have  no  shadows,  be- 
cause the  waves  of  light  would  propagate  themselves 
round  opaque  bodies  as  a  wave  of  water  round  a  rock.  It 
has  been  proved  since  his  time  that  the  waves  of  light  do 
bend  round  opaque  bodies;  but  with  that  we  have  nothing 
now  to  do.  A  sound-wave  certainly  bends  thus  round  an 
obstacle,  though  as  it  diffuses  itself  in  the  air  at  the  back 
of  the  obstacle  it  is  enfeebled  in  power,  the  obstacle  thus 
producing  a  partial  shadow  of  the  sound.  A  railway-train 
passing  through  cuttings  and  long  embankments  exhibits 
great  variations  in  the  intensity  of  the  sound.  The  inter- 
position of  a  hill  in  the  Alps  suffices  to  diminish  materi- 
ally the  sound  of  a  cataract;  it  is  able  sensibly  to  extin- 
guish the  tinkle  of  the  cow-bells.  Still  the  sound-shadow 
is  but  partial,  and  the  marker  at  the  rifle-butts  never  fails 
to  hear  the  explosion,  though  he  is  well  protected  from  the 
ball.  A  striking  example  of  this  diffraction  of  a  sonorous 
wave  was  exhibited  at  Erith  after  the  tremendous  explo- 
sion of  a  powder  magazine  which  occurred  there  in  1864. 
The  village  of  Erith  was  some  miles  distant  from  the  maga- 
zine, but  in  nearly  all  cases  the  windows  were  shattered; 
and  it  was  noticeable  that  the  windows  turned  away  from 
the  origin  of  the  explosion  suffered  almost  as  much  as  those 
1  For  the  sake  of  simplicity,  the  wave  is  shown  broken  at  o'  and  its 
two  halves  straight.  The  surface  of  the  wave,  however,  is  really  a 
curve,  with  its  concavity  turned  in  the  direction  of  its  propagation. 


52  SOUND. 

which,  faced  it.  Lead  sashes  were  employed  in  Erith 
Church,  and  these,  being  in  some  degree  flexible,  enabled 
the  windows  to  yield  to  pressure  without  much  fracture  of 
the  glass.  As  the  sound-wave  reached  the  church  it  sepa- 
rated right  and  left,  and,  for  a  moment,  the  edifice  was 
clasped  by  a  girdle  of  intensely  compressed  air,  every 
window  in  the  church,  front  and  back,  being  bent  inward. 
After  compression,  the  air  within  the  church  no  doubt 
dilated,  tending  to  restore  the  windows  to  their  first  condi- 
tion. The  bending  in  of  the  windows,  however,  produced 
but  a  small  condensation  of  the  whole  mass  of  air  within 
the  church;  the  recoil  was  therefore  feeble  in  comparison 
with  the  pressure,  and  insufficient  to  undo  what  the  latter 
had  accomplished. 

§  8.  Velocity  of  Sound:  relation  to  Density  and  Elas- 
ticity of  Air. 

Two  conditions  determine  the  velocity  of  propagation 
of  a  sonorous  wave;  namely,  the  elasticity  and  the  density 
of  the  medium  through  which  the  wave  passes.  The  elas- 
ticity of  air  is  measured  by  the  pressure  which  it  sustains 
or  can  hold  in  equilibrium.  At  the  sea-level  this  pressure 
is  equal  to  that  of  a  stratum  of  mercury  about  thirty 
inches  high.  At  the  summit  of  Mont  Blanc  the  baro- 
metric column  is  not  much  more  than  half  this  height; 
and,  consequently,  the  elasticity  of  the  air  upon  the  sum- 
mit of  the  mountain  is  not  much  more  than  half  what  it  is 
at  the  sea-level. 

If  we  could  augment  the  elasticity  of  air,  without  at 
the  same  time  augmenting  its  density,  we  should  augment 
the  velocity  of  sound.  Or,  if  allowing  the  elasticity  to 
remain  constant  we  could  diminish  the  density,  we  should 
augment  the  velocity.  Now,  air  in  a  closed  vessel,  where 
it  cannot  expand,  has  its  elasticity  augmented  by  heat, 
while  its  density  remains  unchanged.  Through  such  heated 


INFLUENCE  OF  TEMPERATURE  ON  VELOCITY.      53 

air  sound  travels  more  rapidly  than  through  cold  air.  Again, 
air  free  to  expand  has  its  density  lessened  by  warming,  its 
elasticity  remaining  the  same,  and  through  such  air  sound 
travels  more  rapidly  than  through  cold  air.  This  is  the 
case  with  our  atmosphere  when  heated  by  the  sun. 

The  velocity  of  sound  in  air,  at  the  freezing  tempera- 
ture, is  1,090  feet  a  second. 

At  all  lower  temperatures  the  velocity  is  less  than  this, 
and  at  all  higher  temperatures  it  is  greater.  The  late  M. 
"Wertheim  has  determined  the  velocity  of  sound  in  air  of 
different  temperatures,  and  here  are  some  of  his  results: 

Temperature  Velocity  of 
of  air.  sound. 

0.5°  centigrade 1,089  feet. 

2.10         "          1,091    " 

8.5  "          1,109    " 

12.0  "          1,113    " 

26.6  "          1,140    " 

At  a  temperature  of  half  a  degree  above  the  freezing- 
point  of  water  the  velocity  is  1,089  feet  a  second;  at  a 
temperature  of  26.6  degrees,  it  is  1,140  feet  a  second,  or 
a  difference  of  51  feet  for  26  degrees;  that  is  to  say,  an 
augmentation  of  velocity  of  nearly  two  feet  for  every  sin- 
gle degree  centigrade. 

With  the  same  elasticity  the  density  of  hydrogen  gas 
is  much  less  than  that  of  air,  and  the  consequence  is  that 
the  velocity  of  sound  in  hydrogen  far  exceeds  its  velocity 
in  air.  The  reverse  holds  good  for  heavy  carbonic-acid 
gas.  If  density  and  elasticity  vary  in  the  same  proportion, 
as  the  law  of  Boyle  and  Mariotte  proves  them  to  do  in  air 
when  the  temperature  is  preserved  constant,  they  neutralize 
each  other's  effects;  hence,  if  the  temperature  were  the 
same,  the  velocity  of  sound  upon  the  summits  of  the  high- 
est Alps  would  be  the  same  as  that  at  the  mouth  of  the 
Thames.  But,  inasmuch  as  the  air  above  is  colder  than 
that  below,  the  actual  velocity  on  the  summits  of  the  moun- 


54:  SOUND. 

tains  is  less  than  that  at  the  sea-level.  To  express  this  re- 
sult in  stricter  language,  the  velocity  is  directly  propor- 
tional to  the  square  root  of  the  elasticity  of  the  air;  it  is 
also  inversely  proportional  to  the  square  root  of  the  den- 
sity of  the  air.  Consequently,  as  in  air  of  a  constant 
temperature  elasticity  and  density  vary  in  the  same  pro- 
portion, and  act  oppositely,  the  velocity  of  sound  is  not 
affected  by  a  change  of  density,  if  unaccompanied  by  a 
change  of  temperature. 

There  is  no  mistake  more  common  than  to  suppose  the 
velocity  of  sound  to  be  augmented  by  density.  The  mis- 
take has  arisen  from  a  misconception  of  the  fact  that  in 
solids  and  liquids  the  velocity  is  greater  than  in  gases. 
But  it  is  the  higher  elasticity  of  those  bodies,  in  relation 
to  their  density,  that  causes  sound  to  pass  rapidly  through 
them.  Other  things  remaining  the  same,  an  augmentation 
of  density  always  produces  a  diminution  of  velocity.  Were 
the  elasticity  of  water,  which  is  measured  by  its  compressi- 
bility, only  equal  to  that  of  air,  the  velocity  of  sound  in 
water,  instead  of  being  more  than  quadruple  the  velocity 
in  air,  would  be  only  a  small  fraction  of  that  velocity. 
Both  density  and  elasticity,  then,  must  be  always  borne  in 
mind;  the  velocity  of  sound  being  determined  by  neither 
taken  separately,  but  by  the  relation  of  the  one  to  the 
other.  The  effect  of  small  density  and  high  elasticity  is 
exemplified  in  an  astonishing  manner  by  the  luminiferous 
ether,  which  transmits  the  vibrations  of  light — not  at  the 
rate  of  so  many  feet,  but  at  the  rate  of  nearly  two  hundred 
thousand  miles  a  second. 

Those  who  are  unacquainted  with  the  details  of  scien- 
tific investigation  have  no  idea  of  the  amount  of  labor 
expended  in  the  determination  of  those  numbers  on  which 
important  calculations  or  inferences  depend.  They  have 
no  idea  of  the  patience  shown  by  a  Berzelius  in  deter- 
mining atomic  weights;  by  a  Kegnault  in  determining 


DETERMINATION  OF  VELOCITY.  55 

coefficients  of  expansion;  or  by  a  Joule  in  determining 
the  mechanical  equivalent  of  heat.  There  is  a  morality 
brought  to  bear  upon  such  matters  which,  in  point  of  se- 
verity, is  probably  without  a  parallel  in  any  other  domain 
of  intellectual  action.  Thus,  as  regards  the  determination 
of  the  velocity  of  sound  in  air,  hours  might  be  filled  with 
a  simple  statement  of  the  efforts  made  to  establish  it  with 
precision.  The  question  has  occupied  the  attention  of 
experimenters  in  England,  France,  Germany,  Italy,  and 
Holland.  But  to  the  French  and  Dutch  philosophers  we 
owe  the  application  of  the  last  refinements  of  experimental 
skill  to  the  solution  of  the  problem.  They  neutralized 
effectually  the  influence  of  the  wind;  they  took  into  ac- 
count barometric  pressure,  temperature,  and  hygrometric 
condition.  Sounds  were  started  at  the  same  moment  from 
two  distant  stations,  and  thus  caused  to  travel  from  station 
to  station  through  the  self -same  air.  The  distance  between 
the  stations  was  determined  by  exact  trigonometrical  ob- 
servations, and  means  were  devised  for  measuring  with  the 
utmost  accuracy  the  time  required  by  the  sound  to  pass 
from  the  one  station  to  the  other.  This  time,  expressed 
in  seconds,  divided  into  the  distance  expressed  in  feet,  gave 
1,090  feet  per  second  as  the  velocity  of  sound  through  air 
at  the  temperature  of  0°  centigrade. 

The  time  required  by  light  to  travel  over  all  terrestrial 
distances  is  practically  zero;  and  in  the  experiments  just 
referred  to  the  moment  of  explosion  was  marked  by  the 
flash  of  a  gun,  the  time  occupied  by  the  sound  in  passing 
from  station  to  station  being  the  interval  observed  between 
the  appearance  of  the  flash  and  the  arrival  of  the  sound. 
The  velocity  of  sound  in  air  once  established,  it  is  plain 
that  we  can  apply  it  to  the  determination  of  distances. 
By  observing,  for  example,  the  interval  between  the  ap- 
pearance of  a  flash  of  lightning  and  the  arrival  of  the  ac- 
companying thunder-peal,  we  at  once  determine  the  dis- 


56  SOUND. 

tance  of  the  place  of  discharge.  It  is  only  when  the  inter- 
val between  the  flash  and  peal  is  short  that  danger  from 
lightning  is  to  be  apprehended. 

§  9.  Theoretic  Velocity  calculated  by  Newton. 
Laplace's  Correction. 

We  now  come  to  one  of  the  most  delicate  points  in  the 
whole  theory  of  sound.  The  velocity  through  air  has  been 
determined  by  direct  experiment;  but  knowing  the  elas- 
ticity and  density  of  the  air,  it  is  possible,  without  any 
experiment  at  all,  to  calculate  the  velocity  with  which  a 
sound-wave  is  transmitted  through  it.  Sir  Isaac  Newton 
made  this  calculation,  and  found  the  velocity  at  the  freez- 
ing temperature  to  be  916  feet  a  second.  This  is  about 
one-sixth  less  than  actual  observation  had  proved  the 
velocity  to  be,  and  the  most  curious  suppositions  were 
FIG.  12.  made  to  account  for  the  discrepancy.  Newton 
himself  threw  out  the  conjecture  that  it  was  only 
in  passing  from  particle  to  particle  of  the  air  that 
sound  required  time  for  its  transmission;  that  it 
moved  instantaneously  through  the  particles  them- 
selves. He  then  supposed  the  line  along  which 
sound  passes  to  be  occupied  by  air-particles  for 
one-sixth  of  its  extent,  and  thus  he  sought  to  make 
good  the  missing  velocity.  The  very  art  and 
ingenuity  of  this  assumption  were  sufficient  to 
throw  doubt  on  it;  other  theories  were  therefore 
advanced,  but  the  great  French  mathematician 
Laplace  was  the  first  to  completely  solve  the 
enigma.  I  shall  now  endeavor  to  make  you 
thoroughly  acquainted  with  his  solution. 

Into  this  strong  cylinder  of  glass,  T  u,  Fig. 
12,  which  is  accurately  bored,  and  quite  smooth 
within,  fits  an  air-tight  piston.     By  pushing  the 
piston  down,  I  condense  the  air  beneath  it,  heat  being  at 


NEWTON'S  CALCULATIONS  IN  VELOCITY.  57 

the  same  time  developed.  A  scrap  of  amadou  attached 
to  the  bottom  of  the  piston  is  ignited  by  the  heat  gener- 
ated by  compression.  If  a  bit  of  cotton  wool  dipped 
into  bisulphide  of  carbon  be  attached  to  the  piston,  when 
the  latter  is  forced  down,  a  flash  of  light,  due  to  the  igni- 
tion of  the  bisulphide  of  carbon  vapor,  is  observed  within 
the  tube.  It  is  thus  proved  that  when  air  is  compressed 
heat  is  generated.  By  another  experiment  it  may  be  shown 
that  when  air  is  rarefied  cold  is  developed.  This  brass 
box  contains  a  quantity  of  condensed  air.  I  open  the  cock, 
and  permit  the  air  to  discharge  itself  against  a  suitable 
thermometer;  the  sinking  of  the  instrument  immediately 
declares  the  chilling  of  the  air. 

All  that  you  have  heard  regarding  the  transmission  of 
a  sonorous  pulse  through  air  is,  I  trust,  still  fresh  in  your 
minds.  As  the  pulse  advances  it  squeezes  the  particles  of 
air  together,  and  two  results  follow  from  this  compression. 
Firstly,  its  elasticity  is  augmented  through  the  mere  aug- 
mentation of  its  density.  Secondly,  its  elasticity  is  aug- 
mented by  the  heat  of  compression.  It  was  the  change  of 
elasticity  which  resulted  from  a  change  of  density  that 
Newton  took  into  account,  and  he  entirely  overlooked  the 
augmentation  of  elasticity  due  to  the  second  cause  just 
mentioned.  Over  and  above,  then,  the  elasticity  involved 
in  Newton's  calculation,-  we  have  an  additional  elasticity 
due  to  changes  of  temperature  produced  by  the  sound-wave 
itself.  When  both  are  taken  into  account,  the  calculated 
and  the  observed  velocities  agree  perfectly. 

But  here,  without  due  caution,  we  may  fall  into  the 
gravest  error.  In  fact,  in  dealing  with  Nature,  the  mind 
must  be  on  the  alert  to  seize  all  her  conditions;  otherwise 
we  soon  learn  that  our  thoughts  are  not  in  accordance  with 
her  facts.  It  is  to  be  particularly  noted  that  the  augmen- 
tation of  velocity  due  to  the  changes  of  temperature  pro- 
duced by  the  sonorous  wave  itself  is  totally  different  from 


58  SOUND. 

the  augmentation  arising  from  the  heating  of  the  general 
mass  of  the  air.  The  average  temperature  of  the  air  is 
unchanged  by  the  waves  of  sound.  We  cannot  have  a  con- 
densed pulse  without  having  a  rarefied  one  associated  with 
it.  But  in  the  rarefaction,  the  temperature  of  the  air  is 
as  much  lowered  as  it  is  raised  in  the  condensation.  Sup- 
posing, then,  the  atmosphere  parceled  out  into  such  con- 
densations and  rarefactions,  with  their  respective  tempera- 
tures, an  extraneous  sound  passing  through  such  an  atmos- 
phere would  be  as  much  retarded  in  the  latter  as  accel- 
erated in  the  former,  and  no  variation  of  the  average 
velocity  could  result  from  such  a  distribution  of  temper- 
ature. 

Whence,  then,  does  the  augmentation  pointed  out  by 
Laplace  arise?  I  would  ask  your  best  attention  while  I 
endeavor  to  make  this  knotty  point  clear  to  you.  If  air 
be  compressed  it  becomes  smaller  in  volume;  if  the  press- 
ure be  diminished,  the  volume  expands.  The  force 
which  resists  compression,  and  which  produces  expansion, 
is  the  elastic  force  of  the  air.  Thus  an  external  pressure 
squeezes  the  air-particles  together;  their  own  elastic  force 
holds  them  asunder,  and  the  particles  are  in  equilibrium 
when  these  two  forces  are  in  equilibrium.  Hence  it  is 
that  the  external  pressure  is  a  measure  of  the  elastic  force. 
Let  the  middle  row  of  dots,  Fig.  13,  represent  a  series  of 
air-particles  in  a  state  of  quiescence  between  the  points  a 
and  x.  Then,  because  of  the  elastic  force  exerted  between 
the  particles,  if  any  one  of  them  be  moved  from  its  posi- 
tion of  rest,  the  motion  will  be  transmitted  through  the 
entire  series.  Supposing  the  particle  a  to  be  driven  by  the 
prong  of  a  tuning-fork,  or  some  other  vibrating  body,  to- 
ward x,  so  as  to  be  caused  finally  to  occupy  the  position  af 
in  the  lowest  row  of  particles:  at  the  instant  the  excur- 
sion of  a  commences,  its  motion  begins  to  be  transmitted 
to  &.  In  the  next  following  moments  &  transmits  the 


LAPLACE'S  CORRECTION  ON  NEWTON'S  FORMULA.  59 

motion  to  c,  c  to  d,  d  to  e,  and  so  on.  So  that  by  the 
time  a  has  reached  the  position  a',  the  motion  will  have 
been  propagated  to  some  point  o'  of  the  line  of  particles 
more  or  less  distant  from  of.  The  entire  series  of  particles 
between  of  and  o'  is  then  in  a  state  of  condensation.  The 
distance  a'  o',  over  which  the  motion  has  traveled  during 
the  excursion  of  a  to  a',  will  depend  upon  the  elastic 
force  exerted  between  the  particles.  Fix  your  attention 
on  any  two  of  the  particles,  say  a  and  &.  The  elastic 
force  between  them  may  be  figured  as  a  spiral  spring,  and 
it  is  plain  that  the  more  flaccid  this  spring  the  more 
sluggish  would  be  the  communication  of  the  motion  from 
Fio.  13. 


a  to  &;  while  the  stiff  er  the  spring  the  more  prompt  would 
be  the  communication  of  the  motion.  What  is  true  of  a 
and  b  is  true  for  every  other  pair  of  particles  between  a 
and  o.  Now  the  spring  between  every  pair  of  these  par- 
ticles is  suddenly  stiffened  by  the  heat  developed  along 
the  line  of  condensation,  and  hence  the  velocity  of  prop- 
agation is  augmented  by  this  heat.  Reverting  to  our 
old  experiment  with  the  row  of  boys,  it  is  as  if,  by  the 
very  act  of  pushing  his  neighbor,  the  muscular  rigidity 
of  each  boy's  arm  was  increased,  thus  enabling  him  to 
deliver  his  push  more  promptly  than  he  would  have  done 
without  this  increase  of  rigidity.  The  condensed  portion 
of  a  sonorous  wave  is  propagated  in  the  manner  here 
described,  and  it  is  plain  that  the  velocity  of  propagation 
is  augmented  by  the  heat  developed  in  the  condensation. 


60  SOUND. 

Let  us  now  turn  our  thoughts  for  a  moment  to  the 
propagation  of  the  rarefaction.  Supposing,  as  before,  the 
middle  row  a  a;  to  represent  the  particles  of  air  in  equi- 
librium under  the  pressure  of  the  atmosphere,  and  suppose 
the  particle  a  to  be  suddenly  drawn  to  the  right,  so  as  to 
occupy  the  position  a"  in  the  highest  line  of  dots:  a"  is 
immediately  followed  by  b",  b"  by  c",  c"  by  d" ',  d"  by  e"  ; 
and  thus  the  rarefaction  is  propagated  backward  toward 
#",  reaching  a  point  o"  in  the  line  of  particles  by  the  time 
a  has  completed  its  motion  to  the  right.  Now,  why  does 
b"  follow  a"  when  a"  is  drawn  away  from  it?  Manifestly 
because  the  elastic  force  exerted  between  b"  and  a"  is  less 
than  that  between  b"  and  c".  In  fact,  V  will  be  driven 
after  a"  by  a  force  equal  to  the  difference  of  the  two 
elasticities  between  a"  and  b"  and  between  b"  and  c".  The 
same  remark  applies  to  the  motion  of  c"  after  b",  to  that 
of  d"  after  c",  in  fact,  to  the  motion  of  each  succeeding 
particle  when  it  follows  its  predecessor.  The  greater  the 
difference  of  elasticity  on  the  two  sides  of  any  particle  the 
more  promptly  will  it  follow  its  predecessor.  And  here 
observe  what  the  cold  of  rarefaction  accomplishes.  In  ad- 
dition to  the  diminution  of  the  elastic  force  between  a" 
and  b"  by  the  withdrawal  of  a"  to  a  greater  distance,  there 
is  a  further  diminution  due  to  the  lowering  of  the  tem- 
perature. The  cold  developed  augments  the  difference  of 
elastic  force  on  which  the  propagation  of  the  rarefaction 
depends.  Thus  we  see  that  because  the  heat  developed  in 
the  condensation  augments  the  rapidity  of  the  condensa- 
tion, and  because  the  cold  developed  in  the  rarefaction 
augments  the  rapidity  of  the  rarefaction,  the  sonorous 
wave,  which  consists  of  a  condensation  and  a  rarefaction, 
must  have  its  velocity  augmented  by  the  heat  and  the  cold 
which  it  develops  during  its  own  progress. 

It  is  worth  while  fixing  your  attention  here  upon  the 
fact  that  the  distance  a'  of  to  which  the  motion  has  been 


RATIO   OF  SPECIFIC  HEATS  OF  AIR.  61 

propagated  while  a  is  moving  to  the  position  a'  may  be 
vastly  greater  than  that  passed  over  in  the  same  time  by 
the  particle  itself.  The  excursion  of  a'  may  not  be  more 
than  a  small  fraction  of  an  inch,  while  the  distance  to 
which  the  motion  is  transferred  during  the  time  required 
by  a'  to  perform  this  small  excursion  may  be  many  feet, 
or  even  many  yards.  If  this  point  should  not  appear  al- 
together plain  to  you  now,  it  will  appear  so  by-and-by. 

§  10.  Ratio  of  Specific  Heats  of  Air  deduced  from 
Velocity  of  Sound. 

Having  grasped  this,  even  partially,  I  will  ask  you  to 
accompany  me  to  a  remote  corner  of  the  domain  of  physics, 
with  the  view,  however,  of  showing  that  remoteness  does 
not  imply  discontinuity.  Let  a  certain  quantity  of  air 
at  a  temperature  of  0°,  contained  in  a  perfectly  inexpansi- 
ble  vessel,  have  its  temperature  raised  1°.  Let  the  same 
quantity  of  air,  placed  in  a  vessel  which  permits  the  air 
to  expand  when  it  is  heated — the  pressure  on  the  air  being 
kept  constant  during  its  expansion — also  have  its  tem- 
perature raised  1°.  The  quantities  of  heat  employed  in 
the  two  cases  are  different.  The  one  quantity  expresses 
what  is  called  the  specific  heat  of  air  at  constant  volume; 
the  other  the  specific  heat  of  air  at  constant  pressure.1 
It  is  an  instance  of  the  manner  in  which  apparently  un- 
related natural  phenomena  are  bound  together,  that  from 
the  calculated  and  observed  velocities  of  sound  in  air  we 
can  deduce  the  ratio  of  these  two  specific  heats.  Squaring 
Xewton's  theoretic  velocity  and  the  observed  velocity,  and 
dividing  the  greater  square  by  the  less,  we  obtain  the  ratio 
referred  to.  Calling  the  specific  heat  at  constant  volume 
Cv,and  that  at  constant  pressure  Cp;  calling,  moreover, 

1  See  "  Heat  as  a  Mode  of  Motion,"  chap,  iii, 


62  SOUND. 

^Newton's  calculated  velocity  V,  and  the  observed  velocity 
V,  Laplace  proved  that  — 


Inserting  the  values  of  V  and  V  in  this  equation,  and 
making  the  calculation,  we  find  — 

§-:=- 

Thus,  without  knowing  either  the  specific  heat  at  con- 
stant volume  or  at  constant  pressure,  Laplace  found  the 
ratio  of  the  greater  of  them  to  the  less  to  be  1.42.  It  is 
evident  from  the  foregoing  formulae  that  the  calculated 
velocity  of  sound,  multiplied  by  the  square  root  of  this 
ratio,  gives  the  observed  velocity. 

But  there  is  one  assumption  connected  with  the  deter- 
mination of  this  ratio,  which  must  be  here  brought  clearly 
forth.  It  is  assumed  that  the  heat  developed  by  compres- 
sion remains  in  the  condensed  portion  of  the  wave,  and 
applies  itself  there  to  augment  the  elasticity;  that  no  por- 
tion of  it  is  lost  by  radiation.  If  air  were  a  powerful 
radiator,  this  assumption  could  not  stand.  The  heat  de- 
veloped in  the  condensation  could  not  then  remain  in  the 
condensation.  It  would  radiate  all  round,  lodging  itself 
for  the  most  part  in  the  chilled  and  rarefied  portion  of  the 
wave,  which  would  be  gifted  with  a  proportionate  power 
of  absorption.  Hence  the  direct  tendency  of  radiation 
would  be  to  equalize  the  temperatures  of  the  different 
parts  of  the  wave,  and  thus  to  abolish  the  increase  of  ve- 
locity which  called  forth  Laplace's  correction.1 

•  In  fact,  the  prompt  abstraction  of  the  motion  of  heat  from  the 
condensation,  and  its  prompt  communication  to  the  rarefaction  by  the 
contiguous  luminiferous  ether,  would  prevent  the  former  from  ever 
rising  so  high,  or  the  latter  from  ever  falling  so  low,  in  temperature  as 
it  would  do  if  the  power  of  radiation  was  absent. 


MECHANICAL  EQUIVALENT  OF  HEAT.  63 

§11.  Mechanical  Equivalent  of  Heat  deduced  from 
Velocity  of  Sound. 

The  question,  then,  of  the  correctness  of  this  ratio  in- 
volves the  other  and  apparently  incongruous  question, 
whether  atmospheric  air  possesses  any  sensible  radiative 
power.  If  the  ratio  be'  correct,  the  practical  absence  of 
radiative  power  on  the  part  of  air  is  demonstrated.  How 
then  are  we  to  ascertain  whether  the  ratio  is  correct  or 
not?  By  a  process  of  reasoning  which  illustrates  still  fur- 
ther how  natural  agencies  are  intertwined.  It  was  this 
ratio,  looked  at  by  a  man  of  genius,  named  Mayer,  which 
helped  him  to  a  clearer  and  a  grander  conception  of  the 
relation  and  interaction  of  the  forces  of  inorganic  and  or- 
ganic nature  than  any  philosopher  up  to  his  time  had  at- 
tained. Mayer  was  the  first  to  see  that  the  excess  0.42  of 
fhe  specific  heat  at  constant  pressure  over  that  at  constant 
volume  was  the  quantity  of  heat  consumed  in  the  work 
performed  by  the  expanding  gas.  Assuming  the  air  to  be 
confined  laterally  and  to  expand  in  a  vertical  direction,  in 
which  direction  it  would  simply  have  to  lift  the  weight  of 
the  atmosphere,  he  attempted  to  calculate  the  precise 
amount  of  heat  consumed  in  the  raising  of  this  or  any 
other  weight.  He  thus  sought  to  determine  the  "  mechan- 
ical equivalent  "  of  heat.  In  the  combination  of  his  data 
his  mind  was  clear,  but  for  the  numerical  correctness  of 
these  data  he  was  obliged  to  rely  upon  the  experimenters 
of  his  age.  Their  results,  though  approximately  correct, 
were  not  so  correct  as  the  transcendent  experimental  abil- 
ity of  Regnault,  aided  by  the  last  refinements  of  con- 
structive skill,  afterward  made  them.  Without  changing 
in  the  slightest  degree  the  method  of  his  thought  or  the 
structure  of  his  calculation,  the  simple  introduction  of 
the  exact  numerical  data  into  the  formula  of  Mayer  brings 
out  the  true  mechanical  equivalent  of  heat. 
5 


64  SOUND. 

But  how  are  we  able  to  speak  thus  confidently  of  the 
accuracy  of  this  equivalent?  We  are  enabled  to  do  so  by 
the  labors  of  an  Englishman,  who  worked  at  this  subject 
contemporaneously  with  Mayer;  and  who,  while  animated 
by  the  creative  genius  of  his  celebrated  German  brother, 
enjoyed  also  the  opportunity  of  bringing  the  inspirations 
of  that  genius  to  the  test  of  experiment.  By  the  immortal 
experiments  of  Mr.  Joule,  the  mutual  convertibility  of 
mechanical  work  and  heat  was  first  conclusively  estab- 
lished. And  "  Joule's  equivalent,"  as  it  is  rightly  called, 
considering  the  amount  of  resolute  labor  and  skill  ex- 
pended in  its  determination,  is  almost  identical  with  that 
derived  from  the  formula  of  Mayer. 

§  12.  Absence  of  Radiative  Power  of  Air  deduced  from 

Velocity  of  Sound. 

i 

Consider  now  the  ground  we  have  trodden,  the  curious 
labyrinth  of  reasoning  and  experiment  through  which  we 
have  passed.  We  started  with  the  observed  and  calculated 
velocities  of  sound  in  atmospheric  air.  We  found  Laplace, 
by  a  special  assumption,  deducing  from  these  velocities 
the  ratio  of  the  specific  heat  of  air  at  constant  pressure  to 
its  specific  heat  at  constant  volume.  We  found  Mayer 
calculating  from  this  ratio  the  mechanical  equivalent  of 
heat;  finally,  we  found  Joule  determining  the  same 
equivalent  by  direct  experiments  on  the  friction  of  solids 
and  liquids.  And  what  is  the  result?  Mr.  Joule's  experi- 
ments prove  the  result  of  Mayer  to  be  the  true  one;  they 
therefore  prove  the  ratio  determined  by  Laplace  to  be 
the  true  ratio;  and,  because  they  do  this,  they  prove  at 
the  same  time  the  practical  absence  of  radiative  power  in 
atmospheric  air.  It  seems  a  long  step  from  the  stirring 
of  water,  or  the  rubbing  together  of  iron  plates  in  Joule's 
experiments,  to  the  radiation  of  the  atoms  of  our  atmos- 


ABSENCE  OF  KADIATIVE   POWER  IN  AIR.  65 

phere;  both  questions  are,  however,  connected  by  the  line 
of  reasoning  here  followed  out. 

But  the  true  physical  philosopher  never  rests  content 
with  an  inference  when  an  experiment  to  verify  or  contra- 
vene it  is  possible.  The  foregoing  argument  is  clinched 
by  bringing  the  radiative  power  of  atmospheric  air  to  a 
direct  test.  When  this  is  done,  experiment  and  reasoning 
are  found  to  agree;  air  being  proved  to  be  a  body  sensibly 
devoid  of  radiative  and  absorptive  power.1 

But  here  the  experimenter  on  the  transmission  of 
sound  through  gases  needs  a  word  of  warning.  In  La- 
place's day,  and  long  subsequently,  it  was  thought  that 
gases  of  all  kinds  possessed  only  an  infinitesimal  power  of 
radiation;  but  that  this  is  not  the  case,  is  now  well  estab- 
lished. It  would  be  rash  to  assume  that,  in  the  case  of 
such  bodies  as  ammonia,  aqueous  vapor,  sulphurous  acid, 
and  olefiant  gas,  their  enormous  radiative  powers  do  not 
interfere  with  the  application  of  the  formula  of  Laplace. 
It  behooves  us  to  inquire  whether  the  ratio  of  the  two  spe- 
cific heats  deduced  from  the  velocity  of  sound  in  these 
bodies  is  the  true  ratio;  and  whether,  if  the  true  ratio 
could  be  found  by  other  methods,  its  square  root,  multi- 
plied into  the  calculated  velocity,  would  give  the  observed 
velocity.  From  the  moment  heat  first  appears  in  the  con- 
densation and  cold  in  the  rarefaction  of  a  sonorous  wave  in 
any  of  those  gases,  the  radiative  power  comes  into  play  to 
abolish  the  difference  of  temperature.  The  condensed  part 
of  the  wave  is  on  this  account  rendered  more  flaccid  and 
the  rarefied  part  less  flaccid  than  it  would  otherwise  be, 
and  with  a  sufficiently  high  radiative  power  the  velocity 
of  sound,  instead  of  coinciding  with  that  derived  from  the 
formula  of  Laplace,  must  approximate  to  that  derived 
from  the  more  simple  formula  of  Newton. 

1  "  Heat  a  Mode  of  Motion,"  chap.  x. 


66  SOUND. 

§  13.   Velocity  of  Sound  through  Gases,  Liquids, 
and  Solids. 

To  complete  our  knowledge  of  the  transmission  of 
sound  through  gases,  a  table  is  here  added  from  the  excel- 
lent researches  of  Dulong,  who  employed  in  his  experi- 
ments a  method  which  shall  be  subsequently  explained: 

VELOCITY  OF  SOUND  IN  GASES  AT  THE  TEMPERATURE  OF  0°  C. 

Velocity. 

Air 1,092  feet. 

Oxygen 1,040    " 

Hydrogen 4,164    " 

Carbonicacid 858    " 

Carbonic  oxide 1,107    " 

Protoxide  of  nitrogen 859    " 

Olefiant  gas 1,030    " 

According  to  theory,  the  velocities  of  sound  in  oxygen 
and  hydrogen  are  inversely  proportional  to  the  square 
roots  of  the  densities  of  the  two  gases.  We  here  find  this 
theoretic  deduction  verified  by  experiment.  Oxygen  being 
sixteen  times  heavier  than  hydrogen,  the  velocity  of  sound 
in  the  latter  gas  ought,  according  to  the  above  law,  to  be 
four  times  its  velocity  in  the  former;  hence,  the  velocity 
in  oxygen  being  1,040,  in  hydrogen  calculation  would 
make  it  4,160.  Experiment,  we  see,  makes  it  4,164. 

The  velocity  of  sound  in  liquids  may  be  determined 
theoretically,  as  Newton  determined  its  velocity  in  air; 
for  the  density  of  a  liquid  is  easily  determined,  and  its 
elasticity  can  be  measured  by  subjecting  it  to  compression. 
In  the  case  of  water,  the  calculated  and  the  observed 
velocities  agree  so  closely  as  to  prove  that  the  changes  of 
temperature  produced  by  a  sound-wave  in  water  have  no 
sensible  influence  upon  the  velocity.  In  a  series  of  mem- 
orable experiments  in  the  lake  of  Geneva,  MM.  Colladon 
and  Sturm  determined  the  velocity  of  sound  through 
water,  and  made  it  4,708  feet  a  second.  By  a  mode  of 


VELOCITY  IN  GASES,   LIQUIDS,   AND  SOLIDS.        67 


experiment  which  you  will  subsequently  be  able  to  com- 
prehend, the  late  M.  Wertheim  determined  the  velocity 
through  various  liquids,  and  in  the  following  table  I  have 
collected  his  results: 

TRANSMISSION  OF  SOUND  THROUGH  LIQUIDS. 


Name  of  Liquid. 

Temperature. 

Velocity. 

15°  C 

Feet. 
4714 

30 

5013 

u                        « 

60 

5657 

Sea-water  (artificial) 

20 

4768 

18 

5132 

Solution  of  sulphate  of  soda 

20 

5,194 

Solution  of  carbonate  of  soda  

22 

5,230 

Solution  of  nitrate  of  soda   

21 

5,477 

Solution  of  chloride  of  calcium         

23 

6493 

Common  alcohol  

20 

4.218 

Absolute  alcohol   

23 

3,804 

Spirits  of  turpentine  

24 

3,976 

Sulphuric  ether  

0 

3,801 

We  learn  from  this  table  that  sound  travels  with  dif- 
ferent velocities  through  different  liquids;  that  a  salt 
dissolved  in  water  augments  the  velocity,  and  that  the 
salt  which  produces  the  greatest  augmentation  is  chloride 
of  calcium.  The  experiments  also  teach  us  that  in  water, 
as  in  air,  the  velocity  augments  with  the  temperature.  At 
a  temperature  of  15°  C.,  for  example,  the  velocity  in  Seine 
water  is  4,714  feet,  at  30°  it  is  5,013  feet,  and  at  60° 
5,657  feet  a  second. 

I  have  said  that  from  the  compressibility  of  a  liquid, 
determined  by  proper  measurements,  the  velocity  of  sound 
through  the  liquid  may  be  deduced.  Conversely,  from  the 
velocity  of  sound  in  a  liquid,  the  compressibility  of  the 
liquid  may  be  deduced.  Wertheim  compared  a  series  of 
compressibilities  deduced  from  his  experiments  on  sound 
with  a  similar  series  obtained  directly  by  M.  Grassi.  The 
agreement  of  both,  exhibited  in  the  following  table,  is  a 


68 


SOUND. 


strong  confirmation  of  the  accuracy  of  the  method  pur- 
sued by  Wertheim: 

Cubic  compressibility. 


from  Wertheim's     from  the  direct 
velocity  of  sound,     experiments  of 


Sea-water 0.0000467 

Solution  of  common  salt 0.0000349 

"  carbonate  of  soda 0.0000337 

"  nitrate  of  soda 0 . 0000301 

Absolute  alcohol 0 . 0000947 

Sulphuric  ether 0.0001002 


cper 

M.  Grassi. 
0.0000436 
0.0000321 
0.0000297 
0.0000295 
0.0000991 
0.0001110 


The  greater  the  resistance  which  a  liquid  offers  to  com- 
pression, the  more  promptly  and  forcibly  will  it  return 
to  its  original  volume  after  it  has  been  compressed.  The 
less  the  compressibility,  therefore,  the  greater  is  the  elas- 
ticity, and  consequently,  other  things  being  equal,  the 
greater  the  velocity  of  sound  through  the  liquid. 

We  have  now  to  examine  the  transmission  of  sound 
through  solids.  Here,  as  a  general  rule,  the  elasticity,  as 
compared  with  the  density,  is  greater  than  in  liquids,  and 
consequently  the  propagation  of  sound  is  more  rapid.  In 
the  following  table  the  velocity  of  sound  through  various 
metals,  as  determined  by  Wertheim,  is  recorded: 

VELOCITY  OF  SOUND  THROUGH  METALS. 


Name  of  Metal. 

At  20°  C. 

At  100°  C. 

At  200°  C. 

Lead.  .  . 

4,030 

3,951 

Gold 

5717 

5640 

5619 

Silver 

8553 

8,658 

8  127 

Copper 

11  666 

10,802 

9090 

8815 

8,437 

8079 

Iron                    .          

16.822 

17,386 

15,483 

Iron  wire  (ordinary)  

16.130 

16,728 

Cast  steel  

16,357 

16.153 

15.709 

Steel  wire  (English)  

15.470 

17,201 

16,394 

Steel  wire 

16023 

16443 

As  a  general  rule,  the  velocity  of  sound  through  metals 
is  diminished  by  augmented  temperature;  iron  is,  how- 
ever, a  striking  exception  to  this  rule,  but  it  is  only  within 


INFLUENCE  OF  MOLECULAR  STRUCTURE.     69 

certain  limits  an  exception.  While,  for  example,  a  rise 
of  temperature  from  20°  to  100°  C.  in  the  case  of  copper 
causes  the  velocity  to  fall  from  11,666  to  10,802,  the  same 
rise  produces  in  the  case  of  iron  an  increase  of  velocity 
from  16,882  to  17,386.  Between  100°  and  200°,  how- 
ever, we  see  that  iron  falls  from  the  last  figure  to  15,483. 
In  iron,  therefore,  up  to  a  certain  point,  the  elasticity  is 
augmented  by  heat;  beyond  that  point  it  is  lowered.  Sil- 
ver is  also  an  example  of  the  same  kind. 

The  difference  of  velocity  in  iron  and  in  air  may  be  il- 
lustrated by  the  following  instructive  experiment :  Choose 
one  of  the  longest  horizontal  bars  employed  for  fencing  in 
Hyde  Park;  and  let  an  assistant  strike  the  bar  at  one  end 
while  the  ear  of  the  observer  is  held  close  to  the  bar  at  a 
considerable  distance  from  the  point  struck.  Two  sounds 
will  reach  the  ear  in  succession;  the  first  being  transmit- 
ted through  the  iron  and  the  second  through  the  air.  This 
effect  was  obtained  by  M.  Biot,  in  his  experiments  on  the 
iron  water-pipes  of  Paris. 

The  transmission  of  sound  through  a  solid  depends 
on  the  manner  in  which  the  molecules  of  the  solid  are 
arranged.  If  the  body  be  homogeneous  and  without 
structure,  sound  is  transmitted  through  it  equally  well  in 
all  directions.  But  this  is  not  the  case  when  the  body, 
whether  inorganic  like  a  crystal  or  organic  like  a  tree, 
possesses  a  definite  structure.  This  is  also  true  of  other 
things  than  sound.  Subjecting,  for  example,  a  sphere  of 
wood  to  the  action  of  a  magnet,  it  is  not  equally  affected 
in  all  directions.  It  is  repelled  by  the  pole  of  the  magnet, 
but  it  is  most  strongly  repelled  when  the  force  acts  along 
the  fibre.  Heat  also  is  conducted  with  different  facilities 
in  different  directions  through  wood.  It  is  most  freely 
conducted  along  the  fibre,  and  it  passes  more  freely  across 
the  ligneous  layers  than  along  them.  Wood,  therefore, 
possesses  three  unequal  axes  of  calorific  conduction. 


70 


SOUND. 


These,  established  by  myself,  coincide  with  the  axes  of 
elasticity  discovered  by   Savart.      MM.   Wertheim   and 
Chevandier  have  determined  the  velocity  of  sound  along 
these  three  axes  and  obtained  the  following  results: 
VELOCITY  OF  SOUND  IN  WOOD. 


Name  of  Wood. 

Along  Fibre. 

Across  Rings. 

Along  Rings. 

15467 

4840 

4436 

Fir 

15218 

4382 

2572 

Beech 

10965 

6028 

4G43 

Oak 

12622 

5,036 

4,229 

Pine.     .               

10900 

4611 

2.605 

Elm  

13,516 

4,665 

3,324 

Svcanaore  

14,639 

4,916 

3,728 

Ash  

15,314 

4,567 

4,142 

Alder  

15,306 

4,491 

3,423 

16  677 

5297 

2987 

Maple 

13472 

5047 

3401 

Poplar 

14050 

4600 

3444 

FIG.  14. 


Separating  a  cube  from  the  bark-wood  of  a  good-sized 
tree,  where  the  rings  for  a  short  distance  may  be  regarded 
as  straight:  then,  if  A  K,  Fig. 
14,  be  the  section  of  the  tree, 
the  velocity  of  tho  sound  in 
the  direction  m  n,  through 
such  a  cube,  is  greater  than 
in  the  direction  a  6. 

The  foregoing  table  strik- 
ingly illustrates  the  influence 
of  molecular  structure.  The 
great  majority  of  crystals  show 
differences  of  the  same  kind. 
Such  bodies,  for  the  most  part, 
have  their  molecules  arranged  in  different  degrees  of 
proximity  in  different  directions,  and  where  this  occurs 
there  are  sure  to  be  differences  in  the  transmission  and 
manifestation  of  heat,  light,  electricity,  magnetism,  and 
sound. 


HOOKE'S  ANTICIPATION  OF  THE  STETHOSCOPE.     "(\ 

§  14.  Hooke's  Anticipation  of  the  Stethoscope. 

I  will  conclude  this  lecture  on  the  transmission  of 
sound  through  gases,  liquids,  and  solids,  by  a  quaint  and 
beautiful  extract  from  the  writings  of  that  admirable 
thinker,  Dr.  Robert  Hooke.  It  will  be  noticed  that  the 
philosophy  of  the  stethoscope  is  enunciated  in  the  follow- 
ing passage,  and  another  could  hardly  be  found  which 
illustrates  so  well  that  action  of  the  scientific  imagination 
which,  in  all  great  investigators,  is  the  precursor  and  asso- 
ciate of  experiment: 

"  There  may  also  be  a  possibility,"  writes  Hooke,  "  of 
discovering  the  internal  motions  and  actions  of  bodies  by 
the  sound  they  make.  Who  knows  but  that,  as  in  a  watch, 
we  may  hear  the  beating  of  the  balance,  and  the  running 
of  the  wheels,  and  the  striking  of  the  hammers,  and  the 
grating  of  the  teeth,  and  multitudes  of  other  noises; 
who  knows,  I  say,  but  that  it  may  be  possible  to  discover 
the  motions  of  the  internal  parts  of  bodies,  whether  ani- 
mal, vegetable,  or  mineral,  by  the  sound  they  make;  that 
one  may  discover  the  works  performed  in  the  several 
offices  and  shops  of  a  man's  body,  and  thereby  discover 
what  instrument  or  engine  is  out  of  order,  what  works  are 
going  on  at  several  times,  and  lie  still  at  others,  and  the 
like;  that  in  plants, and  vegetables  one  might  discover  by 
the  noise  the  pumps  for  raising  the  juice,  the  valves  for 
stopping  it,  and  the  rushing  of  it  out  of  one  passage  into 
another,  and  the  like?  I  could  proceed  further,  but  me- 
thinks  I  can  hardly  forbear  to  blush  when  I  consider  how 
the  most  part  of  men  will  look  upon  this:  but,  yet  again, 
I  have  this  encouragement,  not  to  think  all  these  things 
utterly  impossible,  though  never  so  much  derided  by  the 
generality  of  men,  and  never  so  seemingly  mad,  foolish, 
and  phantastic,  that  as  the  thinking  them  impossible  can- 
not much  improve  my  knowledge,  so  the  believing  them 
possible  may,  perhaps,  be  an  occasion  of  taking  notice  of 


72  SOUND. 

such  things  as  another  would  pass  by  without  regard  as 
useless.  And  somewhat  more  of  encouragement  I  have 
also  from  experience,  that  I  have  been  able  to  hear  very 
plainly  the  beating  of  a  man's  heart,  and  it  is  common  to 
hear  the  motion  of  wind  to  and  fro  in  the  guts,  and  other 
small  vessels;  the  stopping  of  the  lungs  is  easily  discov- 
ered by  the  wheezing,  the  stopping  of  the  head  by  the 
humming  and  whistling  noises,  the  slipping  to  and  fro  of 
the  joints,  in  many  cases,  by  crackling,  and  the  like,  as  to 
the  working  or  motion  of  the  parts  one  among  another; 
methinks  I  could  receive  encouragement  from  hearing  the 
hissing  noise  made  by  a  corrosive  menstruum  in  its  opera- 
tion, the  noise  of  fire  in  dissolving,  of  water  in  boiling,  of 
the  parts  of  a  bell  after  that  its  motion  is  grown  quite  in- 
visible as  to  the  eye,  for  to  me  these  motions  and  the 
other  seem  only  to  differ  secundum  magis  minus,  and  so 
to  their  becoming  sensible  they  require  either  that  their 
motions  be  increased,  or  that  the  organ  be  made  more 
nice  and  powerful  to  sensate  and  distinguish  them." 


NOTE  ON  THE  DIFFRACTION  OF  SOUND. 

The  recent  explosion  of  a  powder-laden  barge  in  the  Regent's  Park 
produced  effects  similar  to  those  mentioned  in  §  7.  The  sound-wave 
bent  round  houses  ai\d  broke  the  windows  at  the  back,  the  coalescence 
of  different  portions  of  the  wave  at  special  points  being  marked  by 
intensified  local  action.  Close  to  the  place  where  the  explosion  oc- 
curred the  unconsumed  gunpowder  was  in  the  wave,  and,  as  a  conse- 
quence, the  dismantled  gate-keeper's  lodge  was  girdled  all  round  by  a 
black  belt  of  carbon. 


SUMMARY.  73 


SUMMAKY  OF  CHAPTEK  I. 

THE  sound  of  an  explosion  is  propagated  as  a  wave  or 
pulse  through  the  air. 

This  wave  impinging  upon  the  tympanic  membrane 
causes  it  to  shiver,  its  tremors  are  transmitted  to  the  audi- 
tory nerve,  and  along  the  auditory  nerve  to  the  brain, 
where  it  announces  itself  as  sound. 

A  sonorous  wave  consists  of  two  parts,  in  one  of  which 
the  air  is  condensed,  and  in  the  other  rarefied. 

The  motion  of  the  sonorous  wave  must  not  be  con- 
founded with  the  motion  of  the  particles  which  at  any 
moment  form  the  wave.  During  the  passage  of  the  wave 
every  particle  concerned  in  its  transmission  makes  only  a 
small  excursion  to  and  fro. 

The  length  of  this  excursion  is  called  the  amplitude  of 
the  vibration. 

Sound  cannot  pass  through  a  vacuum. 

A  certain  sharpness  of  shock,  or  rapidity  of  vibration, 
is  needed  for  the  production  of  sonorous  waves  in  air.  It 
is  still  more  necessary  in  hydrogen,  because  the  greater 
mobility  of  this  light  gas  tends  to  prevent  the  formation 
of  condensations  and  rarefactions. 

Sound  is  in  all  respects  reflected  like  light;  it  is  also 
refracted  like  light;  and  it  may,  like  light,  be  condensed 
by  suitable  lenses. 

Sound  is  also  diffracted,  the  sonorous  wave  bending 
round  obstacles;  such  obstacles,  however,  in  part  shade 
off  the  sound. 

Echoes  are  produced  by  the  reflected  waves  of  sound. 


Y4:  SOUND. 

In  regard  to  sound  and  the  medium  through  which 
it  passes,  four  distinct  things  are  to  be  borne  in  mind — 
intensity,  velocity,  elasticity,  and  density. 

The  intensity  is  proportional  to  the  square  of  the  am- 
plitude as  above  defined. 

It  is  also  proportional  to  the  square  of  the  maximum 
velocity  of  the  vibrating  air-particles. 

When  sound  issues  from  a  small  body  in  free  air,  the 
intensity  diminishes  as  the  square  of  the  distance  from 
the  body  increases. 

If  the  wave  of  sound  be  confined  in  a  tube  with  a 
smooth  interior  surface,  it  may  be  conveyed  to  great  dis- 
tances without  sensible  loss  of  intensity. 

The  velocity  of  sound  in  air  depends  on  the  elasticity 
of  the  air  in  relation  to  its  density.  The  greater  the  elas- 
ticity the  swifter  is  the  propagation;  the  greater  the  den- 
sity the  slower  is  the  propagation. 

The  velocity  is  directly  proportional  to  the  square  root 
of  the  elasticity;  it  is  inversely  proportional  to  the  square 
root  of  the  density. 

Hence,  if  elasticity  and  density  vary  in  the  same  pro- 
portion, the  one  will  neutralize  the  other  as  regards  the 
velocity  of  sound. 

That  they  do  vary  in  the  same  proportion  is  proved 
by  the  law  of  Boyle  and  Mariotte;  hence  the  velocity  of 
sound  in  air  is  independent  of  the  density  of  the  air. 

But  that  this  law  shall  hold  good,  it  is  necessary  that 
the  dense  air  and  the  rare  air  should  have  the  same  tem- 
perature. 

The  intensity  of  a  sound  depends  upon  the  density  of 
the  air  in  which  it  is  generated,  but  not  on  that  of  the  air 
in  which  it  is  heard. 

The  velocity  of  sound  in  air  of  the  temperature  0°  C. 
is  1,090  feet  a  second;  it  augments  nearly  2  feet  for  every 
degree  centigrade  added  to  its  temperature. 


SUMMARY.  75 

Hence,  given  the  velocity  of  sound  in  air,  the  tempera- 
ture of  the  air  may  be  readily  calculated. 

The  distance  of  a  fired  cannon  or  of  a  discharge  of 
lightning  may  be  determined  by  observing  the  interval 
which  elapses  between  the  flash  and  the  sound. 

From  the  foregoing,  it  is  easy  to  see  that  if  a  row  of 
soldiers  form  a  circle,  and  discharge  their  pieces  all  at  the 
same  time,  the  sound  will  be  heard  as  a  single  discharge 
by  a  person  occupying  the  centre  of  the  circle. 

But  if  the  men  form  a  straight  row,  and  if  the  observer 
stand  at  one  end  of  the  row,  the  simultaneous  discharge 
of  the  men's  pieces  will  be  prolonged  to  a  kind  of  roar. 

A  discharge  of  lightning  along  a  lengthy  cloud  may 
in  this  way  produce  the  prolonged  roll  of  thunder.  The 
roll  of  thunder,  however,  must  in  part  at  least  be  due  to 
echoes  from  the  clouds. 

The  pupil  will  find  no  difficulty  in  referring  many 
common  occurrences  to  the  fact  that  sound  requires  a  sen- 
sible time  to  pass  through  any  considerable  length  of  air. 
For  example,  the  fall  of  the  axe  of  a  distant  woodcutter 
is  not  simultaneous  with  the  sound  of  the  stroke.  A  com- 
pany of  soldiers  marching  to  music  along  a  road  cannot 
march  in  time,  for  the  notes  do  not  reach  those  in  front 
and  those  behin-d  simultaneously. 

In  the  condensed  portion  of  a  sonorous  wave  the  air  is 
above,  in  the  rarefied  portion  of  the  wave  it  is  below,  its 
average  temperature. 

This  change  of  temperature,  produced  by  the  passage 
of  the  sound-wave  itself,  virtually  augments  the  elasticity 
of  the  air,  and  makes  the  velocity  of  sound  about  ^th 
greater  than  it  would  be  if  there  were  no  change  of  tem- 
perature. 

The  velocity  found  by  Newton,  who  did  not  take  this 
change  of  temperature  into  account,  was  916  feet  a  second. 

Laplace  proved  that  by  multiplying  Newton's  velocity 


76  SOUND. 

by  the  square  root  of  the  ratio  of  the  specific  heat  of  air  at 
constant  pressure  to  its  specific  heat  at  constant  volume, 
the  actual  or  observed  velocity  is  obtained. 

Conversely,  from  a  comparison  of  the  calculated  and 
observed  velocities,  the  ratio  of  the  two  specific  heats  may 
be  inferred. 

The  mechanical  equivalent  of  heat  may  be  deduced 
from  this  ratio;  it  is  found  to  be  the  same  as  that  estab- 
lished by  direct  experiment. 

This  coincidence  leads  to  the  conclusion  that  atmos- 
pheric air  is  devoid  of  any  sensible  power  to  radiate  heat. 
Direct  experiments  on  the  radiative  power  of  air  establish 
the  same  result. 

The  velocity  of  sound  in  water  is  more  than  four  times 
its  velocity  in  air. 

The  velocity  of  sound  in  iron  is  seventeen  times  its 
velocity  in  air. 

The  velocity  of  sound  along  the  fibre  of  pine-wood  is 
ten  times  its  velocity  in  air. 

The  cause  of  this  great  superiority  is  that  the  elastici- 
ties of  the  liquid,  the  metal,  and  the  wood,  as  compared 
with  their  respective  densities,  are  vastly  greater  than  the 
elasticity  of  air  in  relation  to  its  density. 

The  velocity  of  sound  is  dependent  to  some  extent 
upon  molecular  structure.  In  wood,  for  example,  it  is 
conveyed  with  different  degrees  of  rapidity  in  different 
directions. 


CHAPTER  II. 

Physical  Distinction  between  Noise  and  Music. — A  Musical  Tone  pro- 
duced by  Periodic,  Noise  produced  by  Unperiodic,  Impulses. — 
Production  of  Musical  Sounds  by  Taps.— Production  of  Musical 
Sounds  by  Puffs. — Definition  of  Pitch  in  Music. — Vibrations  of  a 
Tuning-Fork;  their  Graphic  Representation  on  Smoked  Glass. — 
Optical  Expression  of  the  Vibrations  of  a  Tuning-Fork. — Descrip- 
tion of  the  Siren.— Limits  of  the  Ear ;  Highest  and  Deepest  Tones. 
— Rapidity  of  Vibration  determined  by  the  Siren. — Determination 
of  the  Lengths  of  Sonorous  Waves. — Wave-Lengths  of  the  Voice 
in  Man  and  Woman. — Transmission  of  Musical  Sounds  through 
Liquids  and  Solids. 

§  1.  Musical  Sounds. 

IN  our  last  chapter  we  considered  the  propagation 
through  air  of  a  sound  of  momentary  duration.  We  have 
to-day  to  consider  continuous  sounds,  and  to  make  our- 
selves in  the  first  place  acquainted  with  the  physical  dis- 
tinction between  noise  and  music.  As  far  as  sensation 
goes,  everybody  knows  the  difference  between  these  two 
things.  But  we  have  now  to  inquire  into  the  causes  of 
sensation,  and  to  make  ourselves  acquainted  with  the  con- 
dition of  the  external  air  which  in  one  case  resolves  itself 
into  music  and  in  another  into  noise. 

We  have  already  learned  that  what  is  loudness  in  our 
sensations  is  outside  of  us  nothing  more  than  width  of 
swing,  or  amplitude,  of  the  vibrating  air-particles.  Every 
other  real  sonorous  impression  of  which  we  are  conscious 
has  its  correlative  without,  as  a  mere  form  or  state  of  the 
atmosphere.  Were  our  organs  sharp  enough  to  see  the 
motions  of  the  air  through  which  an  agreeable  voice  is 
passing,  we  might  see  stamped  upon  that  air  the  conditions 
77 


78  SOUND. 

of  motion  on  which  the  sweetness  of  the  voice  depends. 
In  ordinary  conversation,  also,  the  physical  precedes  and 
arouses  the  psychical;  the  spoken  language,  which  is  to 
give  us  pleasure  or  pain,  which  is  to  rouse  us  to  anger  or 
soothe  us  to  peace,  existing  for  a  time,  between  us  and 
the  speaker,  as  a  purely  mechanical  condition  of  the  inter- 
vening air. 

Noise  affects  us  as  an  irregular  succession  of  shocks. 
We  are  conscious  while  listening  to  it  of  a  jolting  and 
jarring  of  the  auditory  nerve,  while  a  musical  sound 
flows  smoothly  and  without  asperity  or  irregularity.  How 
is  this  smoothness  secured?  By  rendering  the  impulses 
received  by  the  tympanic  membrane  perfectly  periodic. 
A  periodic  motion  is  one  that  repeats  itself.  The  mo- 
tion of  a  common  pendulum,  for  example,  is  periodic, 
but  its  vibrations  are  far  too  sluggish  to  excite  sonorous 
waves.  To  produce  a  musical  tone  we  must  have  a  body 
which  vibrates  with  the  unerring  regularity  of  the  pendu- 
lum, but  which  can  impart  much  sharper  and  quicker 
shocks  to  the  air. 

Imagine  the  first  of  a  series  of  pulses  following  each 
other  at  regular  intervals,  impinging  upon  the  tympanic 
membrane.  It  is  shaken  by  the  shock;  and  a  body  once 
shaken  cannot  come  instantaneously  to  rest.  The  human 
ear,  indeed,  is  so  constructed  that  the  sonorous  motion 
vanishes  with  extreme  rapidity,  but  its  disappearance  is 
not  instantaneous;  and  if  the  motion  imparted  to  the 
auditory  nerve  by  each  individual  pulse  of  our  series  con- 
tinue until  the  arrival  of  its  successor,  the  sound  will  not 
cease  at  all.  The  effect  of  every  shock  will  be  renewed 
before  it  vanishes,  and  the  recurrent  impulses  will  link 
themselves  together  to  a  continuous  musical  sound.  The 
pulses,  on  the  contrary,  which  produce  noise,  are  of  irreg- 
ular strength  and  recurrence.  The  action  of  noise  upon 
the  ear  has  been  well  compared  to  that  of  a  flickering  light 


NOISE  AND  MUSIC.  79 

upon  the  eye,  both  being  painful  through  the  sudden  and 
abrupt  changes  which  they  impose  upon  their  respective 
nerves. 

The  only  condition  necessary  to  the  production  of  a 
musical  sound  is  that  the  pulses  should  succeed  each  other 
in  the  same  interval  of  time.  No  matter  what  its  origin 
may  be,  if  this  condition  be  fulfilled  the  sound  becomes 
musical.  If  a  watch,  for  example,  could  be  caused  to  tick 
with  sufficient  rapidity — say  one  hundred  times  a  second 
— the  ticks  would  lose  their  individuality  and  blend  to  a 
musical  tone.  And  if  the  strokes  of  a  pigeon's  wings  could 
be  accomplished  at  the  same  rate,  the  progress  of  the  bird 
through  the  air  would  be  accompanied  by  music.  In  the 
humming-bird  the  necessary  rapidity  is  attained;  and  when 
we  pass  on  from  birds  to  insects,  where  the  vibrations  are 
more  rapid,  we  have  a  musical  note  as  the  ordinary  accom- 
paniment of  the  insects'  flight.1  The  puffs  of  a  locomotive 
at  starting  follow  each  other  slowly  at  first,  but  they  soon 
increase  so  rapidly  as  to  be  almost  incapable  of  being 
counted.  If  this  increase  could  continue  up  to  fifty  or 
sixty  puffs  a  second,  the  approach  of  the  engine  would  be 
heralded  by  an  organ-peal  of  tremendous  power. 

§  2.  Musical  Sounds  produced  l>y  Taps. 

Galileo  produced  a  musical  sound  by  passing  a  knife 
over  the  edge  of  a  piastre.  The  minute  serration  of  the 
coin  indicated  the  periodic  character  of  the  motion,  which 
consisted  of  a  succession  of  taps  quick  enough  to  produce 
sonorous  continuity.  Every  schoolboy  knows  how  to  pro- 
duce a  note  with  his  slate-pencil.  I  will  not  call  it  musical, 
because  this  term  is  usually  associated  with  pleasure,  and 
the  sound  of  the  pencil  is  not  pleasant. 

The  production  of  a  musical  sound  by  taps  is  usually 

1  According  to  Burmeister,  through  the  injection  and  ejection  of  air 
into  and  from  the  cavity  of  the  chest. 


80 


SOUND. 


FIG.  15. 


effected  by  causing  the  teeth  of  a  rotating  wheel  to  strike 
in  quick  succession  against  a  card.  This  was  first  illus- 
trated by  the  celebrated  Robert  Hooke,1  and  nearer  our 
own  day  by  the  eminent  French  experimenter  Savart. 
We  will  confine  ourselves  to 
homelier  modes  of  illustration. 
This  gyroscope  is  an  instru- 
ment consisting  mainly  of  a 
heavy  brass  ring,  d,  Fig.  15, 
loading  the  circumference  of 
a  disk,  through  which,  and  at 
right  angles  to  its  surface, 
passes  a  steel  axis,  delicately 
supported  at  its  two  ends.  By 
coiling  a  string  round  the  axis, 
and  drawing  it  vigorously  out, 
the  ring  is  caused  to  spin 
rapidly;  and  along  with  it  ro- 
tates a  small-toothed  wheel,  w. 
On  touching  this  wheel  with 
the  edge  of  a  card,  c,  a  musical 
sound  of  exceeding  shrillness 
is  produced.  I  place  my  thumb 
for  a  moment  against  the  ring;  the  rapidity  of  its  rotation 

1  On  July  27,  1681,  "  Mr.  Hooke  showed  an  experiment  of  making 
musical  and  other  sounds  by  the  help  of  teeth  of  brass  wheels ;  which 
teeth  were  made  of  equal  bigness  for  musical  sounds,  but  of  unequal 
for  vocal  sounds."— (Birch's  "  History  of  the  Royal  Society,"  p.  96,  pub- 
lished in  1757.) 

The  following  extract  is  taken  from  the  "  Life  of  Hooke,"  which  pre- 
cedes his  "Posthumous  Works,"  published  in  1705,  by  Richard  Waller, 
Secretary  of  the  Royal  Society :  "  In  July  the  same  year  he  (Dr.  Hooke) 
showed  a  way  of  making  musical  and  other  sounds  by  the  striking  of 
the  teeth  of  several  brass  wheels,  proportionally  cut  as  to  their  num- 
bers, and  turned  very  fast  round,  in  which  it  was  observable  that  the 
equal  or  proportional  stroaks  of  the  teeth,  that  is,  2  to  1,  4  to  3,  etc., 
made  the  musical  notes,  but  the  unequal  stroaks  of  the  teeth  more 
answered  the  sound  of  the  voice  in  speaking." 


MUSICAL  SOUNDS  PRODUCED  BY  TAPS.  81 

is  thereby  diminished,  and  this  is  instantly  announced  by 
a  lowering  of  the  pitch  of  the  note.  By  checking  the  mo- 
tion still  more,  the  pitch  is  lowered  still  further.  We  are 
here  made  acquainted  with  the  important  fact  that  the 
pitch  of  a  note  depends  upon  the  rapidity  of  its  pulses.1 
At  the  end  of  the  experiment  you  hear  the  separate  taps 
of  the  teeth  against  the  card,  their  succession  not  being 
quick  enough  to  produce  that  continuous  flow  of  sound 
which  is  the  essence  of  music.  A  screw  with  a  milled 
head  attached  to  a  whirling  table,  and  caused  to  rotate, 
produces  by  its  taps  against  a  card  a  note  almost  as  clear 
and  pure  as  that  obtained  from  the  toothed  wheel  of  the 
gyroscope. 

The  production  of  a  musical  sound  by  taps  may  also  be 
pleasantly  illustrated  in  the  following  way:  In  this  vice 
are  fixed  vertically  two  pieces  of  sheet-lead,  with  their 
horizontal  edges  a  quarter  of  an  inch  apart.  I  lay  a  bar 
of  brass  across  them,  permitting  it  to  rest  upon  the  edges, 
and,  tilting  the  bar  a  little,  set  it  in  oscillation  like  a  see- 
saw. After  a  time,  if  left  to  itself,  it  comes  to  rest.  But 
suppose  the  bar  on  touching  the  lead  to  be  always  tilted 
upward  by  a  force  issuing  from  the  lead  itself,  it  is  plain 
that  the  vibrations  would  then  be  rendered  permanent. 
Now  such  a  force  is  brought  into  play  when  the  bar  is 
heated.  On  its  then  touching  the  lead  the  heat  is  commu- 
nicated, a  sudden  jutting  upward  of  the  lead  at  the  point 
of  contact  being  the  result.  Hence  an  incessant  tilting  of 
the  bar  from  side  to  side,  so  long  as  it  continues  sufficiently 
hot.  Substituting  for  the  brass  bar  the  heated  fire-shovel 
shown  in  Fig.  16,  the  same  effect  is  produced. 

In  its  descent  upon  the  lead  the  bar  taps  it  gently,  the 
taps  being  so  slow  that  you  may  readily  count  them.  But 

>  Galileo,  finding  the  number  of  notches  on  his  metal  to  be  great 
•when  the  pitch  of  the  note  •was  high,  inferred  that  the  pitch  depended 
on  the  rapidity  of  the  impulses. 


82  SOUND. 

a  mass  of  metal  differently  shaped  may  be  caused  to 
vibrate  more  briskly,  and  the  taps  to  succeed  each  other 
more  rapidly.  When  such  a  heated  rocker,  Fig.  17,  is 
placed  upon  a  block  of  lead,  the  taps  hasten  to  a  loud  rattle. 

FIG.  16. 


When,  with  the  point  of  a  file,  the  rocker  is  pressed  against 
the  lead,  the  vibrations  are  rendered  more  rapid,  and  the 
taps  link  themselves  together  to  a  deep  musical  tone. 
A  second  rocker,  which  oscillates  more  quickly  than  the 

PIG.  17. 


last,  produces  music  without  any  other  pressure  than  that 
due  to  its  own  weight.  Pressing  it,  however,  with  the 
file,  the  pitch  rises,  until  a  note  of  singular  force  and 


MUSICAL  SOUNDS  PRODUCED  BY  PUFFS.  83 

purity  fills  the  room.  Relaxing  the  pressure,  the  pitch 
instantly  falls;  resuming  the  pressure,  it  again  rises;  and 
thus  by  the  alternation  of  the  pressure  we  obtain  great 
variations  of  tone.  Nor  are  such  rockers  essential.  Al- 
lowing one  face  of  the  clean,  square  end  of  a  heated  poker 
to  rest  upon  the  block  of  lead,  a  rattle  is  heard;  causing 
another  face  to  rest  upon  the  block,  a  clear  musical  note 
is  obtained.  The  two  faces  have  been  beveled  differ- 
ently by  a  file,  so  as  to  secure  different  rates  of  vibration.1 
This  curious  effect  was  discovered  by  Schwartz  and  Tre- 
velyan. 

§  3.  Musical  Sounds  produced  ly  Puffs. 

Prof.  Robison  was  the  first  to  produce  a  musical  sound 
by  a  quick  succession  of  puffs  of  air.  His  device  was 
the  first  form  of  an  instrument  which  will  soon  be  intro- 
duced to  you  under  the  name  of  the  siren.  Robison  de- 
scribes his  experiment  in  the  following  words :  "  A  stop- 
cock was  so  constructed  that  it  opened  and  shut  the  passage 
of  a  pipe  720  times  in  a  second.  The  apparatus  was  fitted 
to  the  pipe  of  a  conduit  leading  from  the  bellows  to  the 
wind-chest  of  an  organ.  The  air  was  simply  allowed  to 
pass  gently  along  this  pipe  by  the  opening  of  the  cock. 
When  this  was  repeated  720  times  in  a  second,  the  sound 
g  in  alt  was  most  smoothly  uttered,  equal  in  sweetness  to 

»  When  a  rough  tide  rolls  in  upon  a  pebble  beach,  as  at  Blackgang 
Chine  or  Freshwater  Gate,  in  the  Isle  of  Wight,  the  rounded  stones  are 
carried  up  the  slope  by  the  impetus  of  the  water,  and  when  the  wave  re- 
treats the  pebbles  are  dragged  down.  Innumerable  collisions  thus  ensue 
of  irregular  intensity  and  recurrence.  The  union  of  these  shocks  im- 
presses us  as  a  kind  of  scream.  Hence  the  line  in  Tennyson's  "Maud :" 

"  Now  to  the  scream  of  a  maddened  beach  dragged  down  by  the  wave." 
The  height  of  the  note  depends  in  some  measure  upon  the  size  of  the 
pebble,  varying  from  a  kind  of  roar — heard  when  the  stones  are  large — 
to  a  scream  ;  from  a  scream  to  a  noise  resembling  that  of  frying  bacon; 
and  from  this,  when  the  pebbles  are  so  small  as  to  approach  the  state 
of  gravel,  to  a  mere  hiss.  The  roar  of  the  breaking  wave  itself  is  mainly 
due  to  the  explosion  of  bladders  of  air. 


84  SOUND. 

a  clear  female  voice.  When  the  frequency  was  reduced 
to  360,  the  sound  was  that  of  a  clear  but  rather  a  harsh 
man's  voice.  The  cock  was  now  altered  in  such  a  manner 
that  it  never  shut  the  hole  entirely,  but  left  about  one- 
third  of  it  open.  When  this  was  repeated  720  times  in  a 
second,  the  sound  was  uncommonly  smooth  and  sweet. 
When  reduced  to  360,  the  sound  was  more  mellow  than 
any  man's  voice  of  the  same  pitch." 

But  the  difficulty  of  obtaining  the  necessary  speed 
renders  another  form  of  the  experiment  preferable.  A 
disk  of  Bristol  board,  B,  Fig.  18,  twelve  inches  in  diam- 
eter, is  perforated  at  equal  intervals  along  a  circle  near 
its  circumference.  The  disk,  being  strengthened  by  a 

FIG.  18. 


backing  of  tin,  can  be  attached  to  a  whirling  table,  and 
caused  to  rotate  rapidly.  The  individual  holes  then  dis- 
appear, blending  themselves  into  a  continuous  shaded 
circle.  Immediately  over  this  circle  is  placed  a  bent  tube, 
m,  connected  with  a  pair  of  acoustic  bellows.  The  disk 
is  now  motionless,  the  lower  end  of  the  tube  being  im- 
mediately over  one  of  the  perforations  of  the  disk.  If, 
therefore,  the  bellows  be  worked,  the  wind  will  pass  from 
m  through  the  hole  underneath.  But  if  the  disk  be  turned 
a  little,  an  unperforated  portion  of  the  disk  comes  under 
the  tube,  the  current  of  air  being  then  intercepted.  As 
the  disk  is  slowly  turned,  successive  perforations  are 
brought  under  the  tube,  and  whenever  this  occurs  a  puff 
of  air  gets  through.  On  rendering  the  rotation  rapid, 


MUSICAL  SOUNDS  PRODUCED  BY  PUFFS.  85 

the  puffs  succeed  each  other  in  very  quick  succession,  pro- 
ducing pulses  in  the  air  which  blend  to  a  continuous 
musical  note,  audible  to  you  all.  Mark  how  the  note 
varies.  When  the  whirling  table  is  turned  rapidly  the 
sound  is  shrill;  when  its  motion  is  slackened  the  pitch 
immediately  falls.  If  instead  of  a  single  glass  tube  there 
were  two  of  them,  as  far  apart  as  two  of  our  orifices,  so 
that  whenever  the  one  tube  stood  over  an  orifice,  the  other 
should  stand  over  another,  it  is  plain  that  if  both  tubes 
were  blown  through,  we  should,  on  turning  the  disk,  get  a 
puff  through  two  holes  at  the  same  time.  The  intensity  of 
the  sound  would  be  thereby  augmented,  but  the  pitch 
would  remain  unchanged.  The  two  puffs  issuing  at  the 
same  instant  would  act  in  concert,  and  produce  a  greater 
effect  than  one  upon  the  ear.  And  if  instead  of  two  tubes 
we  had  ten  of  them,  or  better  still,  if  we  had  a  tube  for 
every  orifice  in  the  disk  the  puffs  from  the  entire  series 
would  all  issue,  and  would  be  all  cut  off  at  the  same  time. 
These  puffs  would  produce  a  note  of  far  greater  intensity 
than  that  obtained  by  the  alternate  escape  and  interruption 
of  the  air  from  a  single  tube.  In  the  arrangement  now 
before  you,  Fig.  19,  there  are  nine  tubes  through  which 

FIG.  19. 


the  air  is  urged — through  nine  apertures,  therefore,  puffs 
escape  at  once.  On  turning  the  whirling  table,  and  alter- 
nately increasing  and  relaxing  its  speed,  the  sound  rises 
and  falls  like  the  loud  wail  of  a  changing  wind. 


86  SOUND. 

§  4.  Musical  Sounds  produced  by  a  Tuning-fork. 

Various  other  means  may  be  employed  to  throw  the 
air  into  a  state  of  periodic  motion.  A  stretched  string 
pulled  aside  and  suddenly  liberated  imparts  vibrations 
to  the  air  which  succeed  each  other  in  perfectly  regular 
intervals.  A  tuning-fork  does  the  same.  When  a  bow  is 
drawn  across  the  prongs  of  this  tuning-fork,  Tig.  20,  the 
resin  of  the  bow  enables  the  hairs  to  grip  the  prong, 
which  is  thus  pulled  aside.  But  the  resistance  of  the  prong 
soon  becomes  too  strong,  and  it  starts  suddenly  back; 
it  is,  however,  immediately  laid  hold  of  again  by  the  bow, 


to  start  back  once  more  as  soon  as  its  resistance  becomes 
great  enough.  This  rhythmic  process,  continually  re- 
peated during  the  passage  of  the  bow,  finally  throws  the 
fork  into  a  state  of  intense  vibration,  and  the  result  is 
a  musical  note.  A  person  close  at  hand  could  see  the 
fork  vibrating;  a  deaf  person  bringing  his  hand  suffi- 
ciently near  would  feel  the  shivering  of  the  air.  Or  caus- 
ing its  vibrating  prong  to  touch  a  card,  the  taps  against 
the  card  link  themselves,  as  in  the  case  of  the  gyroscope, 
to  a  musical  sound,  the  fork  coming  rapidly  to  rest.  What 
we  call  silence  expresses  this  absence  of  motion. 


THE  TUNING-FOKK.  87 

When  the  tuning-fork  is  first  excited  the  sound  issues 
from  it  with  maximum  loudness,  becoming  gradually  fee- 
bler as  the  fork  continues  to  vibrate.     A  person  close  to 
the  fork  can  notice  at  the  same  time  that  the  amplitude, 
or  space  through  which  the  prongs  oscillate,  becomes  grad- 
ually less  and  less.    But  the  most  expert  ear  in  this  assem- 
bly can  detect  no  change  in  the  pitch  of  the  note.     The  \ 
(lowering  of  the  intensity  of  a  note  does  not  therefore  \ 
imply  the  lowering  of  its  pitch.     In  fact,  though  the 


I 


amplitude  changes,  the  rate  of  vibration  remains  the  same. 
Pitch  and  intensity  must  therefore  be  held  distinctly   » 
apart;  the  latter  depends  solely  upon  the  amplitude,  the  I 
former  solely  upon  the  rapidity  of  vibration. 

This  tuning-fork  may  be  caused  to  write  the  story  of 
its  own  motion.  Attached  to  the  side  of  one  of  its  prongs, 
F,  Fig.  21,  is  a  thin  strip  of  sheet-copper  which  tapers  to 


FIG.  21. 


a  point.  "When  the  tuning-fork  is  excited  it  vibrates, 
and  the  strip  of  metal  accompanies  it  in  its  vibration. 
The  point  of  the  strip  being  brought  gently  down  upon  a 
piece  of  smoked  glass,  it  moves  to  and  fro  over  the 
smoked  surface,  leaving  a  clear  line  behind.  As  long  as 
the  hand  is  kept  motionless,  the  point  merely  passes  to 
and  fro  over  the  same  line;  but  it  is  plain  that  we  have 
only  to  draw  the  fork  along  the  glass  to  produce  a  sinu- 
ous line,  Fig.  21. 

When  this  process  is  repeated  without  exciting  the  fork 
afresh,  the  depth  of  the  indentations  diminishes.  The 
sinuous  line  approximates  more  and  more  to  a  straight  one. 


88 


SOUND. 


This  is  the  visual  expression  of  decreasing  amplitude. 
When  the  sinuosities  entirely  disappear,  the  amplitude  has 
become  zero,  and  the  sound,  which  depends  upon  the  am- 
plitude, ceases  altogether. 

To  M.  Lissajous  we  are  indebted  for  a  very  beautiful 
method  of  giving  optical  expression  to  the  vibrations  of  a 
tuning-fork.  Attached  to  one  of  the  prongs  of  a  very  large 
fork  is  a  small  metallic  mirror,  r,  Fig.  22,  the  other  prong 
being  loaded  with  a  piece  of  metal  to  establish  equi- 
librium. Permitting  a  slender  beam  of  intense  light  to 
fall  upon  the  mirror,  the  beam  is  thrown  back  by  reflec- 


FIG.  22. 


tion.  In  my  hands  is  held  a  small  looking-glass,  which 
receives  the  reflected  beam,  and  from  which  it  is  again 
reflected  to  the  screen,  forming  a  small  luminous  disk 
upon  the  white  surface.  The  disk  is  perfectly  motionless ; 
but  the  moment  the  fork  is  set  in  vibration  the  reflected 
beam  is  tilted  rapidly  up  and  down,  the  disk  describing  a 
band  of  light  three  feet  long.  The  length  of  the  band 
depends  on  the  amplitude  of  the  vibration,  and  you  see 
it  gradually  shorten  as  the  motion  of  the  fork  is  expended. 
It  remains,  however,  a  straight  line  as  long  as  the  glass 
is  held  in  a  fixed  position.  But  on  suddenly  turning  the 


OPTICAL  ILLUSTRATIONS.  89 

glass  so  as  to  make  the  beam  travel  from  left  to  right  over 
the  screen,  you  observe  the  straight  line  instantly  resolved 
into  a  beautiful  luminous  ripple  m  n.  A  luminous  im- 
pression once  made  upon  the  retina  lingers  there  for  the 
tenth  of  a  second;  if  then  the  time  required  to  transfer 
the  elongated  image  from  side  to  side  of  the  screen  be 
less  than  the  tenth  of  a  second,  the  wavy  line  of  light 
will  occupy  for  a  moment  the  whole  width  of  the  screen. 
Instead  of  permitting  the  beam  from  the  lamp  to  issue 
through  a  single  aperture,  it  may  be  caused  to  issue 
through  two  apertures,  about  half  an  inch  asunder,  thus 
projecting  two  disks  of  light,  one  above  the  other,  upon  the 
screen.  When  the  fork  is  excited  and  the  mirror  turned, 
we  have  a  brilliant  double  sinuous  line  running  over  the 
dark  surface,  Fig.  23.  Turning  the  diaphragm  so  as  to 
FIG.  23. 


place  the  two  disks  beside  each  other,  on  exciting  the  fork 
and  moving  the  mirror,  we  obtain  a  beautiful  interlacing 
of  the  two  sinuous  lines,  Fig.  24. 
FIG.  24. 


§  5.  The  Waves  of  Sound. 

How  are  we  to  picture  to  ourselves  the  condition  of  the 
air  through  which  this  musical  sound  is  passing?  Imagine 
one  of  the  prongs  of  the  vibrating  fork  swiftly  advancing; 
it  compresses  the  air  immediately  in  front  of  it,  and  when 


90 


SOUND. 


it  retreats  it  leaves  a  partial  vacuum  behind,  the  process 
being  repeated  by  every  subsequent  advance  and  retreat. 
The  whole  function  of  the  tuning-fork  is  to  carve  the  air 
into  these  condensations  and  rarefactions,  and  they,  as  they 
are  formed,  propagate  themselves  in  succession  through 
the  air.  A  condensation  with  its  associated  rarefaction 
constitutes,  as  already  stated,  a  sonorous  wave.  In  water 
the  length  of  a  wave  is  measured  from  crest  to  crest; 
while,  in  the  case  of  sound,  the  wave-length  is  the  distance 
between  two  successive  condensations.  The  condensation 
of  the  sound-wave  corresponds  to  the  crest,  while  the  rare- 
faction of  the  sound-wave  corresponds  to  the  sinus,  or  de- 
pression, of  the  water-wave.  Let  the  dark  spaces,  a,  b,  c, 
d,  Fig.  25,  represent  the  condensations,  and  the  light  ones, 


a',  b',  c',  d',  the  rarefactions  of  the  waves  issuing  from 
the  fork  A  B:  the  wave-length  would  then  be  measured 
from  a  to  b,  from  b  to  c,  or  from  c  to  d. 

§  6.  Definition  of  Pitch:  Determination  of  Rates  of 
Vibration. 

When  two  notes  from  two  distinct  sources  are  of  the 
same  pitch,  their  rates  of  vibration  are  the  same.  If,  for 
example,  a  string  yield  *he  same  note  as  a  tuning-fork,  it 
is  because  they  vibrate  with  the  same  rapidity;  and  if  a 
fork  yield  the  same  note  as  the  pipe  of  an  organ  or  the 


THE  SIREN.  91 

tongue  of  a  concertina,  it  is  because  the  vibrations  of  the 
fork  in  the  one  case  are  executed  in  precisely  the  same 
time  as  the  vibrations  of  the  column  of  air,  or  of  the 
tongue,  in  the  other.  The  same  holds  good  for  the  human 
voice.  If  a  string  and  a  voice  yield  the  same  note,  it  is 
because  the  vocal  chords  of  the  singer  vibrate  in  the  same 
time  as  the  string  vibrates.  Is  there  any  way  of  deter- 
mining the  actual  number  of  vibrations  corresponding  to 
a  musical  note?  Can  we  infer  from  the  pitch  of  a  string, 
of  an  organ-pipe,  of  a  tuning-fork,  or  of  the  human  voice, 
the  number  of  waves  which  it  sends  forth  in  a  second? 
This  very  beautiful  problem  is  capable  of  the  most  com- 
plete solution. 

§  7.  The  Siren:  Analysis  of  the  Instrument. 

By  the  rotation  of  a  perforated  pasteboard  disk,  it  has 
been  proved  to  you  that  a  musical  sound  is  produced  by  a 
quick  succession  of  puffs.  Had  we  any  means  of  register- 
ing the  number  of  revolutions  accomplished  by  that  disk 
in  a  minute,  we  should  have  in  it  a  means  of  determining 
the  number  of  puffs  per  minute  due  to  a  note  of  any  de- 
terminate pitch.  The  disk,  however,  is  but  a  cheap  sub- 
stitute for  a  far  more  perfect  apparatus,  which  requires  no 
whirling  table,  and  which  registers  its  own  rotations  with 
the  most  perfect  accuracy. 

I  will  take  the  instrument  asunder,  so  that  you  may 
see  its  various  parts.  A  brass  tube,  t,  Fig.  26,  leads  into 
a  round  box,  c,  closed  at  the  top  by  a  brass  plate  a  b. 
This  plate  is  perforated  with  four  series  of  holes,  placed 
along  four  concentric  circles.  The  innermost  series  con- 
tains 8,  the  next  10,  the  next  12,  and  the  outermost  16 
.orifices.  When  we  blow  into  the  tube  t,  the  air  escapes 
through  the  orifices,  and  the  problem  now  before  us  is  to 
convert  these  continuous  currents  into  discontinuous  puffs. 
This  is  accomplished  by  means  of  a  brass  disk  d  e,  also 


92 


SOUND. 


FIG.  26. 


perforated  with  8,  10,  12,  and  16  holes,  at  the  same  dis- 
tances from  the  centre  and  with  the  same  intervals  be- 
tween them  as  those  in  the  top  of  the  box  c.  Through 
the  centre  of  the  disk  passes  a  steel  axis,  the  two  ends  of 
which  are  smoothly  beveled 
off  to  points  at  p  and  p'. 
My  object  now  is  to  cause 
this  perforated  disk  to  rotate 
over  the  perforated  top  a  b 
of  the  box  c.  You  will  un- 
derstand how  this  is  done  by 
observing  how  the  instru- 
ment is  put  together. 

In  the  centre  of  a  &,  Fig. 
26,  is  a  depression  x  sunk  in 
steel,  smoothly  polished  and 
intended  to  receive  the  end 
p'  of  the  axis.  I  place  the 
end  p'  in  this  depression, 
and,  holding  the  axis  up- 
right, bring  down  upon  its 
upper  end  p  a  steel  cap, 
finely  polished  within,  which 
holds  the  axis  at  the  top, 
the  pressure  both  at  top  and 
bottom  being  so  gentle,  and 
the  polish  of  the  touching 
surfaces  so  perfect,  that  the 
disk  can  rotate  with  an  ex- 
ceedingly small  amount  of 
friction.  At  c,  Fig.  27,  is 
the  cap  which  fits  on  to  the  upper  end  of  the  axis  p  p'. 
In  this  figure  the  disk  d  e  is  shown  covering  the  top  of  the 
cylinder  c.  You  may  neglect  for  the  present  the  wheel- 
work  of  the  figure.  Turning  the  disk  d  e  slowly  round,  its 


ANALYSIS  OF  THE  SIREN. 


93 


FIG.  27. 


perforations  may  be  caused  to  coincide  or  not  coincide 
with  those  of  the  cylinder  underneath.  As  the  disk  turns 
its  orifices  come  alternately  over  the  perforations  of  the 
cylinder,  and  over  the  spaces  between  the  perforations. 
Hence  it  is  plain  that  ii 
air  were  urged  into  c, 
and  if  the  disk  could  be 
caused  to  rotate  at  the 
same  time,  we  should 
accomplish  our  object, 
and  carve  into  puffs  the 
streams  of  air.  In  this 
beautiful  instrument 
the  disk  is  caused  to  ro- 
tate by  the  very  air  cur- 
rents which  it  renders 
intermittent.  This  is 
done  by  the  simple  de- 
vice of  causing  the  per- 
forations to  pass  oblique- 
ly through  the  top  of 
the  cylinder  c,  and  also 
obliquely,  but  opposite- 
ly inclined,  through  the 
rotating  disk  d  e.  The 
air  is  thus  caused  to  is- 
sue from  c,  not  verti- 
cally, but  in  side  cur- 
rents, which  impinge 
against  the  disk  and 
drive  it  round.  In  this  way,  by  its  passage  through  the 
siren,  the  air  is  moulded  into  sonorous  waves. 

Another  moment  will  make  you  acquainted  with  the 
recording  portion  of  the  instrument.  At  the  upper  part 
of  the  steel  axis  p  pf,  Fig.  27,  is  a  screw  s,  working  into  a 


9±  SOUND. 

pair  of  toothed  wheels  (see  when  the  back  of  the  instru- 
ment is  turned  toward  you).  As  the  disk  and  its  axis 
turn,  these  wheels  rotate.  In  front  you  simply  see  two 
graduated  dials,  Fig.  28,  each  furnished  with  an  index  like 
the  hands  of  a  clock.  These  indexes  record  the  number  of 
revolutions  executed  by  the  disk  in  any  given  time.  By 
pushing  the  button  a  or  b  the  wheel-work  is  thrown  into 
or  out  of  action,  thus  starting  or  suspending,  in  a  moment, 
the  process  of  recording.  Finally,  by  the  pins  m,  n,  o,  p, 
Fig.  27,  any  series  of  orifices  in  the  top  of  the  cylinder  c 
can  be  opened  or  closed  at  pleasure.  By  pressing  m,  one 
series  is  opened ;  by  pressing  n,  another.  By  pressing  two 
keys,  two  series  of  orifices  are  opened;  by  pressing  three 
keys,  three  series;  and  by  pressing  all  the  keys,  puffs  are 
caused  to  issue  from  the  four  series  simultaneously.  The 
perfect  instrument  is  now  before  you,  and  your  knowledge 
of  it  is  complete. 

This  instrument  received  the  name  of  siren  from  its 
inventor,  Cagniard  de  la  Tour.    The  one  now  before  you 

is  the  siren  as  greatly 
improved  by  Dove.  The 
pasteboard  siren,  whose 
performance  you  have  al- 
ready heard,  was  devised 
by  Seebeck,  who  gave 
the  instrument  various 
interesting  forms,  and 
executed  with  it  many 
important  experiments. 
Let  us  now  make  the 
siren  sing.  By  pressing 
the  key  m,  the  outer  series  of  apertures  in  the  cylinder  c 
is  opened,  and  by  working  the  bellows,  the  air  is  caused  to 
impinge  against  the  disk.  It  begins  to  rotate,  and  you 
hear  a  succession  of  puffs  which  follow  each  other  so 


EXPERIMENTS  ON  PITCH.  95 

slowly  that  they  may  be  counted.  But  as  the  motion  aug- 
ments, the  puffs  succeed  each  other  with  increasing  rapid- 
ity, and  at  length  you  hear  a  deep  musical  note.  As  the 
velocity  of  rotation  increases  the  note  rises  in  pitch;  it  is 
now  very  clear  and  full,  and  as  the  air  is  urged  more  vig- 
orously, it  becomes  so  shrill  as  to  be  painful.  Here  we 
have  a  further  illustration  of  the  dependence  of  pitch  on 
rapidity  of  vibration.  I  touch  the  side  of  the  disk  and 
lower  its  speed;  the  pitch  falls  instantly.  Continuing  the 
pressure  the  tone  continues  to  sink,  ending  in  the  discon- 
tinuous puffs  with  which  it  began. 

Were  the  blast  sufficiently  powerful  and  the  siren 
sufficiently  free  from  friction,  it  might  be  urged  to  higher 
and  higher  notes,  until  finally  its  sound  would  become 
inaudible  to  human  ears.  This,  however,  would  not  prove 
the  absence  of  vibratory  motion  in  the  air;  but  would 
rather  show  that  our  auditory  apparatus  is  incompetent  to 
take  up  and  translate  into  sound  vibrations  whose  rapidity 
exceeds  a  certain  limit.  The  ear,  as  we  shall  immediately 
learn,  is  in  this  respect  similar  to  the  eye. 

By  means  of  this  siren  we  can  determine  with  extreme 
accuracy  the  rapidity  of  vibration  of  any  sonorous  body. 
It  may  be  a  vibrating  string,  an  organ-pipe,  a  reed,  or  the 
human  voice.  Operating  delicately,  we  might  even  deter- 
mine from  the  hum  of  an  insect  the  number  of  times  it 
flaps  its  wings  in  a  second.  I  will  illustrate  the  subject 
by  determining  in  your  presence  a  tuning-fork's  rapidity 
of  vibration.  From  the  acoustic  bellows  I  urge  the  air 
through  the  siren,  and,  at  the  same  time,  draw  my  bow 
across  the  fork.  Both  now  sound  together,  the  tuning- 
fork  yielding  at  present  the  highest  note.  But  the  pitch 
of  the  siren  gradually  rises,  and  at  length  you  hear 
the  "  beats  "  so  well  known  to  musicians,  which  indicate 
that  the  two  notes  are  not  wide  apart  in  pitch.  These 
beats  become  slower  and  slower;  now  they  entirely 
7 


96  SOUND. 

vanish,  both  notes  blending  as  it  were  to  a  single  stream 
of  sound. 

All  this  time  the  clock-work  of  the  siren  has  remained 
out  of  action.  As  the  second  hand  of  a  watch  crosses 
the  number  60,  the  clock-work  is  set  going  by  pushing  the 
button  a.  We  will  allow  the  disk  to  continue  its  rota- 
tion for  a  minute,  the  tuning-fork  being  excited  from 
time  to  time  to  assure  you  that  the  unison  is  preserved. 
The  second  hand  again  approaches  60;  as  it  passes  that 
number  the  clock-work  is  stopped  by  pushing  the  button  b; 
and  then,  recorded  on  the  dials,  we  have  the  exact  number 
of  revolutions  performed  by  the  disk.  The  number  is 
1,440.  But  the  series  of  holes  open  during  the  experi- 
ment numbers  16;  for  every  revolution,  therefore,  we  had 
16  puffs  of  air,  or  16  waves  of  sound.  Multiplying  1,440 
by  16,  we  obtain  23,040  as  the  number  of  vibrations  exe- 
cuted by  the  tuning-fork  in  a  minute.  Dividing  this  by 
60,  we  find  the  number  of  vibrations  executed  in  a  second 
to  be  384. 

§  8.  Determination  of  Wave-lengths:  Time  of  Vibration. 

Having  determined  the  rapidity  of  vibration,  the 
length  of  the  corresponding  sonorous  wave  is  found  with 
the  utmost  facility.  Imagine  a  tuning-fork  vibrating  in 
free  air.  At  the  end  of  a  second  from  the  time  it  com- 
menced its  vibrations  the  foremost  wave  would  have 
reached  a  distance  of  1,090  feet  in  air  of  the  freezing 
temperature.  In  the  air  of  a  room  which  has  a  tempera- 
ture of  about  15°  C.,  it  would  reach  a  distance  of  1,120 
in  a  second.  In  this  distance,  therefore,  are  embraced 
384  sonorous  waves.  Dividing  1,120  by  384,  we  find  the 
length  of  each  wave  to  be  nearly  3  feet.  Determining  in 
this  way  the  rates  of  vibration  of  the  four  tuning-forks 
now  before  you,  we  find  them  to  be  256,  320,  384,  and 
512;  these  numbers  corresponding  to  wave-lengths  of 


LENGTHS  OF  SOUND-WAVES.  97 

4  feet  4  inches,  3  feet  6  inches,  2  feet  11  inches,  and  2  feet 
2  inches  respectively.  The  waves  generated  by  a  man's 
voice  in  common  conversation  are  from  8  to  12  feet,  those 
of  a  woman's  voice  are  from  2  to  4  feet  in  length.  Hence 
a  woman's  ordinary  pitch  in  the  lower  sounds  of  conversa- 
tion is  more  than  an  octave  above  a  man's;  in  the  higher 
sounds  it  is  two  octaves. 

And  here  it  is  important  to  note  that  by  the  term  vi- 
brations are  meant  complete  ones;  and  by  the  term  sonor- 
ous wave  are  meant  a  condensation  and  its  associated 
rarefaction.  By  a  vibration  an  excursion  to  and  fro  of 
the  vibrating  body  is  to  be  understood.  Every  wave  gen- 
erated by  such  a  vibration  bends  the  tympanic  membrane 
once  in  and  once  out.  These  are  the  definitions  of  a  vi- 
bration and  of  a  sonorous  wave  employed  in  England  and 
Germany.  In  France,  however,  a  vibration  consists  of  an 
excursion  of  the  vibrating  body  in  one  direction,  whether 
to  or  fro.  The  French  vibrations,  therefore,  are  only  the 
halves  of  ours,  and  we  therefore  call  them  semi-vibrations. 
In  all  cases  throughout  these  chapters,  when  the  word  vi- 
bration is  employed  without  qualification,  it  refers  to  com- 
plete vibrations. 

During  the  time  required  by  each  of  those  sonorous 
waves  to  pass  entirely  over  a  particle  of  air,  that  particle 
accomplishes  one  complete  vibration.  It  is  at  one  moment 
pushed  forward  into  the  condensation,  while  at  the  next 
moment  it  is  urged  back  into  the  rarefaction.  The  time 
required  by  the  particle  to  execute  a  complete  oscillation 
is,  therefore,  that  required  by  the  sonorous  wave  to  move 
through  a  distance  equal  to  its  own  length.  Supposing 
the  length  of  the  wave  to  be  eight  feet,  and  the  velocity 
of  sound  in  air  of  our  present  temperature  to  be  1,120  feet 
a  second,  the  wave  in  question  will  pass  over  its  own  length 
of  air  in  -j-j^th  of  a  second:  this  is  the  time  required  by 
every  air-particle  that  it  passes  to  complete  an  oscillation. 


98  SOUND. 

In  air  of  a  definite  density  and  elasticity  a  certain 
length,  of  wave  always  corresponds  to  the  same  pitch. 
But  supposing  the  density  or  elasticity  not  to  be  uniform ; 
supposing,  for  example,  the  sonorous  waves  from  one  of 
our  tuning-forks  to  pass  from  cold  to  hot  air:  an  instant 
augmentation  of  the  wave-length  would  occur,  without 
any  change  of  pitch,  for  we  should  have  no  change  in  the 
rapidity  with  which  the  waves  would  reach  the  ear.  Con- 
versely with  the  same  length  of  wave  the  pitch  would  be 
higher  in  hot  air  than  in  cold,  for  the  succession  of  the 
waves  would  be  quicker.  In  an  atmosphere  of  hydrogen 
waves  of  a  certain  length  would  produce  a  note  nearly  two 
octaves  higher  than  waves  of  the  same  length  in  air;  for, 
in  consequence  of  the  greater  rapidity  of  propagation,  the 
number  of  impulses  received  in  a  given  time  in  the  one 
case  would  be  nearly  four  times  the  number  received  in 
the  other. 

§  9.  Definition  of  an  Octave. 

Opening  the  innermost  and  outermost  series  of  the 
orifices  of  our  siren,  and  sounding  both  of  them,  either 
together  or  in  succession,  the  musical  ears  present  at  once 
detect  the  relationship  of  the  two  sounds.  They  notice 
immediately  that  the  sound  which  issues  from  the  circle  of 
sixteen  orifices  is  the  octave  of  that  which  issues  from  the 
circle  of  eight.  But  for  every  wave  sent  forth  by  the  lat- 
ter, two  waves  are  sent  forth  by  the  former.  In  this  way 
we  prove  that  the  physical  meaning  of  the  term  "  octave  " 
is,  that  it  is  a  note  produced  by  double  the  number  of 
vibrations  of  its  fundamental.  By  multiplying  the  vibra- 
tions of  the  octave  by  two,  we  obtain  its  octave,  and  by 
a  continued  multiplication  of  this  kind  we  obtain  a  series 
of  numbers  answering  to  a  series  of  octaves.  Starting, 
for  example,  from  a  fundamental  note  of  100  vibra- 
tions, we  should  find,  by  this  continual  multiplication,  that 


LIMITS  OF  THE  HUMAN  EAR.  99 

a  note  five  octaves  above  it  would  be  produced  by  3,200 
vibrations.    Thus: 

100    Fundamental  note. 
2 

200    1st  octave. 


400    3d  octave. 
2 

800    3d  octave. 
2 

1600    4th  octave. 


3200    5th  octave. 

This  result  is  more  readily  obtained  by  multiplying  the 
vibrations  of  the  fundamental  note  by  the  fifth  power  of 
two.  In  a  subsequent  chapter  we  shall  return  to  this 
question  of  musical  intervals.  For  our  present  purpose 
it  is  only  necessary  to  define  an  octave. 

§  10.  Limits  of  the  Ear;  and  of  Musical  Sounds. 

The  ear's  range  of  hearing  is  limited  in  both  directions. 
Savart  fixed  the  lower  limit  at  eight  complete  vibrations  a 
second;  and  to  cause  these  slowly  recurring  vibrations  to 
link  themselves  together,  he  was  obliged  to  employ  shocks 
of  great  power.  By  means  of  a  toothed  wheel  and  an 
associated  counter,  he  fixed  the  upper  limit  of  hearing  at 
24,000  vibrations  a  second.  Helmholtz  has  recently  fixed 
the  lower  limit  at  16  vibrations,  and  the  higher  at  38,000 
vibrations,  a  second.  By  employing  very  small  tuning- 
forks,  the  late  M.  Depretz  showed  that  a  sound  correspond- 
ing to  38,000  vibrations  a  second  is  audible.1  Starting 
from  the  note  16,  and  multiplying  continually  by  2,  or 
1  The  error  of  Savart  consists,  according  to  Helmholtz,  in  having 
adopted  an  arrangement  in  which  overtones  (described  in  Chapter  III.) 
were  mistaken  for  the  fundamental  one. 


100  SOUND. 

more  compendiously  raising  2  to  the  llth  power,  and  mul- 
tiplying this  by  16,  we  should  find  that  at  11  octaves 
above  the  fundamental  note  the  number  of  vibrations 
would  be  32,768.  Taking,  therefore,  the  limits  assigned 
by  Helmholtz,  the  entire  range  of  the  human  ear  em- 
braces about  eleven  octaves.  But  all  the  notes  comprised 
within  these  limits  cannot  be  employed  in  music.  The 
practical  range  of  musical  sounds  is  comprised  between 
40  and  4,000  vibrations  a  second,  which  amounts,  in  round 
numbers,  to  seven  octaves.1 

The  limits  of  hearing  are  different  in  different  persons. 
AVhile  endeavoring  to  estimate  the  pitch  of  certain  sharp 
sounds,  Dr.  "VVollaston  remarked  in  a  friend  a  total  insensi- 
bility to  the  sound  of  a  small  organ-pipe,  which,  in  respect 
to  acuteness,  was  far  within  the  ordinary  limits  of  hearing. 
The  sense  of  hearing  of  this  person  terminated  at  a  note 
four  octaves  above  the  middle  E  of  the  pianoforte.  The 
squeak  of  the  bat,  the  sound  of  a  cricket/  even  the  chirrup 
of  the  common  house-sparrow,  are  unheard  by  some  people 
who  for  lower  sounds  possess  a  sensitive  ear.  A  difference 
of  a  single  note  is  sometimes  sufficient  to  produce  the 
change  from  sound  to  silence.  "  The  suddenness  of  the 
transition,"  writes  Wollaston,  "  from  perfect  hearing  to 
total  want  of  perception,  occasions  a  degree  of  surprise 

1  "The  deepest  tone  of  orchestra  instruments  is  the  E  of  the  double- 
bass,  with  41|  vibrations.  The  new  pianos  and  organs  go  generally  as 
far  as  O,  with  33  vibrations;  new  grand  pianos  may  reach  A11,  with 
27-J-  vibrations.  In  large  organs  a  lower  octave  is  introduced,  reaching 
to  C»,  with  16|  vibrations.  But  the  musical  character  of  all  these  tones 
under  E  is  imperfect,  because  they  are  near  the  limit  where  the  power 
of  the  ear  to  unite  the  vibrations  to  a  tone  ceases.  In  height  the  piano- 
forte reaches  to  alv,  with  3,520  vibrations,  or  sometimes  to  cv.  with  4,224 
vibrations.  The  highest  note  of  the  orchestra  is  probably  the  dv  of  the 
piccolo  flute,  with  4,752  vibrations." — (Helmholtz,  "  Tonempfindungen," 
p.  30.)  In  this  notation  we  start  from  C,  with  66  vibrations,  calling  the 
first  lower  octave  C1,  and  the  second  C« ;  and  calling  the  first  highest 
octave  c,  the  second  c1,  the  third  c11,  the  fourth  c»»,  etc.  In  England  the 
deepest  tone,  Mr.  Macfarren  informs  me,  is  not  E,  but  A,  a  fourth  above  it. 


DRUM  OF  THE  EAR.  101 

which  renders  an  experiment  of  this  kind  with  a  series  of 
small  pipes  among  several  persons  rather  amusing.  It  is 
curious  to  observe  the  change  of  feeling  manifested  by 
various  individuals  of  the  party,  in  succession,  as  the 
sounds  approach  and  pass  the  limits  of  their  hearing. 
Those  who  en  joy  a  temporary  triumph  are  often  compelled, 
in  their  turn,  to  acknowledge  to  how  short  a  distance  their 
little  superiority  extends."  "  Nothing  can  be  more  sur- 
prising," writes  Sir  John  Herschel,  "  than  to  see  two  per- 
sons, neither  of  them  deaf,  the  one  complaining  of  the 
penetrating  shrillness  of  a  sound,  while  the  other  main- 
tains there  is  no  sound  at  all.  Thus,  while  one  person  men- 
tioned by  Dr.  "Wollaston  could  but  just  hear  a  note  four 
octaves  above  the  middle  E  of  the  pianoforte,  others  have 
a  distinct  perception  of  sounds  full  two  octaves  higher. 
The  chirrup  of  the  sparrow  is  about  the  former  limit;  the 
cry  of  the  bat  about  an  octave  above  it;  and  that  of  some 
insects  probably  another  octave."  In  "  The  Glaciers  of 
the  Alps  "  I  have  referred  to  a  case  of  short  auditory 
range,  noticed  by  myself  in  crossing  the  Wengern  Alp  in 
company  with  a  friend.  The  grass  at  each  side  of  the  path 
swarmed  with  insects,  which  to  me  rent  the  air  with  their 
shrill  chirruping.  My  friend  heard  nothing  of  this,  the 
insect-music  lying  beyond  his  limit  of  audition. 

§  11.  Drum  of  the  Ear.     The  Eustachian  Tube. 

Behind  the  tympanic  membrane  exists  a  cavity — the 
drum  of  the  ear — in  part  crossed  by  a  series  of  bones,  and 
in  part  occupied  by  air.  This  cavity  communicates  with 
the  mouth  by  means  of  a  duct  called  the  Eustachian  tube. 
This  tube  is  generally  closed,  the  air-space  behind  the  tym- 
panic membrane  being  thus  shut  off  from  the  external  air. 
If,  under  these  circumstances,  the  external  air  becomes 
denser,  it  will  press  the  tympanic  membrane  inward.  If, 
on  the  other  hand,  the  air  outside  becomes  rarer,  while  the 


102  SOUND. 

Eustachian  tube  remains  closed,  the  membrane  will  be 
pressed  outward.  Pain  is  felt  in  both  cases,  and  partial 
deafness  is  experienced.  I  once  crossed  the  Stelvio  Pass 
by  night  in  company  with  a  friend  who  complained  of 
acute  pain  in  the  ears.  On  swallowing  his  saliva  the  pain 
instantly  disappeared.  By  the  act  of  swallowing  the 
Eustachian  tube  is  opened,  and  thus  equilibrium  is  estab- 
lished between  the  external  and  internal  pressure. 

It  is  possible  to  quench  the  sense  of  hearing  of  low 
sounds  by  stopping  the  nose  and  mouth,  and  trying  to  ex- 
pand the  chest,  as  in  the  act  of  inspiration.  'This  effort 
partially  exhausts  the  space  behind  the  tympanic  mem- 
brane, which  is  then  thrown  into  a  state  of  tension  by  the 
pressure  of  the  outward  air.  A  similar  deafness  to  low 
sounds  is  produced  when  the  nose  and  mouth  are  stopped, 
and  a  strong  effort  is  made  to  expire.  In  this  case  air  is 
forced  through  the  Eustachian  tube  into  the  drum  of  the 
ear,  the  tympanic  membrane  being  distended  by  the  press- 
ure of  the  internal  air.  The  experiment  may  be  made  in 
a  railway  carriage,  when  the  low  rumble  will  vanish  or  be 
greatly  enfeebled,  while  the  sharper  sounds  are  heard  with 
undiminished  intensity.  Dr.  AYollaston  was  expert  in 
closing  the  Eustachian  tube,  and  leaving  the  space  behind 
the  tympanic  membrane  occupied  by  either  compressed  or 
rarefied  air.  He  was  thus  able  to  cause  his  deafness  to 
continue  for  any  required  time  without  effort  on  his  part, 
always,  however,  abolishing  it  by  the  act  of  swallowing. 
A  sudden  concussion  may  produce  deafness  by  forcing  air 
either  into  or  out  of  the  drum  of  the  ear,  and  this  may 
account  for  a  fact  noticed  by  myself  in  one  of  my  Al- 
pine rambles.  In  the  summer  of  1858,  jumping  from 
a  cliff  on  to  what  was  supposed  to  be  a  deep  snow-drift, 
I  came  into  rude  collision  with  a  rock  which  the  snow 
barely  covered.  The  sound  of  the  wind,  the  rush  of  the 
glacier-torrents,  and  all  the  other  noises  which  a  sunny  day 


THE  DOUBLE  SIEEN.  103 

awakes  upon  the  mountains,  instantly  ceased.  I  couldi 
hardly  hear  the  sound  of  my  guide's  voice.  This  deafness 
continued  for  half  an  hour;  at  the  end  of  which  time  the 
blowing  of  the  nose  opened,  I  suppose,  the  Eustachian 
tube,  and  restored,  with  the  quickness  of  magic,  the  in- 
numerable murmurs  which  filled  the  air  around  me. 

Light,  like  sound,  is  excited  by  pulses  or  waves;  and 
lights  of  different  colors,  like  sounds  of  different  pitch, 
are  excited  by  different  rates  of  vibration.  But  in  its 
width  of  perception  the  ear  exceedingly  transcends  the 
eye;  for  while  the  former  ranges  over  eleven  octaves,  but 
little  more  than  a  single  octave  is  possible  to  the  latter. 
The  quickest  vibrations  which  strike  the  eye,  as  light, 
have  only  about  twice  the  rapidity  of  the  slowest ; l  where- 
as the  quickest  vibrations  which  strike  the  ear,  as  a  musical 
sound,  have  more  than  two  thousand  times  the  rapidity 
of  the  slowest. 

§  12.  Helmholtz's  Double  Siren. 

Prof.  Dove,  as  we  have  seen,  extended  the  utility  of 
the  siren  of  Cagniard  de  la  Tour,  by  providing  it  with 
four  series  of  orifices  instead  of  one.  By  doubling  all  its 
parts,  Helmholtz  has  recently  added  vastly  to  the  power 
of  the  instrument.  The  double  siren,  as  it  is  called,  is 
now  before  you,  Fig.  29  (next  page).  It  is  composed  of 
two  of  Dove's  sirens,  c  and  c',  one  turned  upside  down. 
You  will  recognize  in  the  lower  siren  the  instrument  with 
which  you  are  already  acquainted.  The  disks  of  the  two 
sirens  have  a  common  axis,  so  that  when  one  disk  rotates 
the  other  rotates  with  it.  As  in  the  former  case,  the  num- 
ber of  revolutions  is  recorded  by  clock-work  (omitted  in 
the  figure).  When  air  is  urged  through  the  tube  t'  the 

1  It  is  hardly  necessary  to  remark  that  the  quickest  vibrations  and 
shortest  waves  correspond  to  the  extreme  violet,  while  the  slowest  vibra- 
tions and  longest  waves  correspond  to  the  extreme  red,  of  the  spectrum. 


104 


THE  DOUBLE  SIREN.  105 

upper  siren  alone  sounds;  when  urged  through  t,  'the 
lower  one  only  sounds;  when  it  is  urged  simultaneously 
through  t'  and  t,  both  the  sirens  sound.  With  this  instru- 
ment, therefore,  we  are  able  to  introduce  much  more 
varied  combinations  than  with  the  former  one.  Helm- 
holtz  has  also  contrived  a  means  by  which  not  only  the 
disk  of  the  upper  siren,  but  the  box  c'  above  the  disk,  can 
be  caused  to  rotate.  This  is  effected  by  a  toothed  wheel 
and  pinion,  turned  by  a  handle.  Underneath  the  handle 
is  a  dial  with  an  index,  the  use  of  which  will  be  subse- 
quently illustrated. 

Let  us  direct  our  attention  for  the  present  to  the  upper 
siren.  By  means  of  an  India-rubber  tube,  the  orifice  t'  is 
connected  with  an  acoustic  bellows,  and  air  is  urged  into 
c'.  Its  disk  turns  round,  and  we  obtain  with  it  all  the 
results  already  obtained  with  Dove's  siren.  The  pitch  of 
the  note  is  uniform.  Turning  the  handle  above,  so  as  to 
cause  the  orifices  of  the  cylinder  c'  to  meet  those  of  the 
disk,  the  two  sets  of  apertures  pass  each  other  more  rapidly 
than  when  the  cylinder  stood  still.  An  instant  rise  of 
pitch  is  the  result.  By  reversing  the  motion,  the  orifices 
are  caused  to  pass  each  other  more  slowly  than  when  c'  is 
motionless,  and  in  this  case  you  notice  an  instant  fall  of 
pitch  when  the  handle  is  turned.  Thus,  by  imparting  in 
quick  alternation  a  right-handed  and  left-handed  motion 
to  the  handle,  we  obtain  successive  rises  and  falls  of  pitch. 
An  extremely  instructive  effect  of  this  kind  may  be  ob- 
served at  any  railway  station  on  the  passage  of  a  rapid 
train.  During  its  approach  the  sonorous  waves  emitted  by 
the  whistle  are  virtually  shortened,  a  greater  number  of 
them  being  crowded  into  the  ear  in  a  given  time.  During 
its  retreat  we  have  a  virtual  lengthening  of  the  sonorous 
waves.  The  consequence  is,  that,  when  approaching,  the 
whistle  sounds  a  higher  note,  and  when  retreating  it  sounds 
a  lower  note,  than  if  the  train  were  still.  A  fall  of  pitch, 


106  SOUND. 

therefore,  is  perceived  as  the  train  passes  the  station.1  This 
is  the  basis  of  Doppler's  theory  of  the  colored  stars.  He 
supposes  that  all  stars  are  white,  but  that  some  of  them 
are  rapidly  retreating  from  us,  thereby  lengthening  their 
luminif  erous  waves  and  becoming  red.  Others  are  rapidly 
approaching  us,  thereby  shortening  their  waves,  and  be- 
coming green  or  blue.  The  ingenuity  of  this  theory  is 
extreme,  but  its  correctness  is  more  than  doubtful. 

§  13.  Transmission  of  Musical  Sounds  by  Liquids  and 
Solids. 

We  have  thus  far  occupied  ourselves  with  the  trans- 
mission of  musical  sounds  through  air.  They  are  also 
transmitted  by  liquids  and  solids.  When  a  tuning-fork 
screwed  into  a  little  wooden  foot  vibrates,  nobody,  except 
the  persons  closest  to  it,  hears  its  sound.  On  dipping  the 
foot  into  a  glass  of  water  a  musical  sound  is  audible:  the 
vibrations  having  been  transmitted  through  the  water  to 
the  air.  The  tube  M  N,  Fig.  30,  three  feet  long,  is  set  up- 
right upon  a  wooden  tray  A  B.  The  tube  ends  in  a  funnel 
at  the  top,  and  is  now  filled  with  water  to  the  brim.  The 
fork  F  is  thrown  into  vibration,  and  on  dipping  its  foot 
into  the  funnel  at  the  top  of  the  tube,  a  musical  sound 
swells  out.  I  must  so  far  forestall  matters  as  to  remark 
that  in  this  experiment  the  tray  is  the  real  sounding  body. 
It  has  been  thrown  into  vibration  by  the  fork,  but  the 
vibrations  have  been  conveyed  to  the  tray  by  the  water. 
Through  the  same  medium  vibrations  are  communicated 
to  the  auditory  nerve,  the  terminal  filaments  of  which  are 
immersed  in  a  liquid:  substituting  mercury  for  water,  a 
similar  result  is  obtained. 

1  Experiments  on  this  subject  were  first  made  by  M.  Buys  Ballot  on 
the  Dutch  railway,  and  subsequently  by  Mr.  Scott  Russell  in  this  coun- 
try. Doppler's  idea  is  now  applied  to  determine,  from  changes  of  wave- 
length, motions  in  the  sun  and  fixed  stars. 


MUSICAL  SOUNDS  THROUGH  LIQUIDS. 


107 


FIG.  30. 


The  siren  has  received  its  name  from  its  capacity  to 
sing  under  water.  A  vessel  now  in  front  of  the  table  is 
half  filled  with  water,  in  which  a  siren  is  wholly  immersed. 
"When  a  cock  is  turned  the  water  from  the  pipes  which 
supply  the  house  forces  itself  through  the  instrument.  Its 
disk  is  now  rotating,  and  a  sound  of  rapidly  augmenting 
pitch  issues  from  the  vessel.  The  pitch  rises  thus  rapidly 
because  the  heavy  and  powerfully  pressed  water  soon  drives 
the  disk  up  to  its  maximum  speed  of  rotation.  When 
the  supply  is  les- 
sened, the  mo- 
tion relaxes  and 
the  pitch  falls. 
Thus,  by  alter- 
nately opening 
and  closing  the 
cock,  the  song 
of  the  siren  is 
caused  to  rise 
and  fall  in  a  wild 
and  melancholy 
manner.  You 
would  not  con- 
sider such  a 
sound  likely  to 
woo  mariners  to 
their  doom. 

The  transmis- 
sion of  musical 
sounds  through 
solid  bodies  is  also  capable  of  easy  and  agreeable  illustra- 
tion. Before  you  is  a  wooden  rod,  thirty  feet  long,  passing 
from  the  table  through  a  window  in  the  ceiling,  into  the 
open  air  above.  The  lower  end  of  the  rod  rests  upon  a 
wooden  tray,  to  which  the  musical  vibrations  of  a  body  ap- 


108  SOUND. 

plied  to  the  upper  end  of  the  rod  are  to  be  transferred. 
An  assistant  is  above,  with  a  tuning-fork  in  his  hand.  He 
strikes  the  fork  against  a  pad;  it  vibrates,  but  you  hear 
nothing.  He  now  applies  the  stem  of  the  fork  to  the  end 
of  the  rod,  and  instantly  the  wooden  tray  upon  the  table  is 
rendered  musical.  The  pitch  of  the  sound,  moreover,  is 
exactly  that  of  the  tuning-fork;  the  wood  has  been  passive 
as  regards  pitch,  transmitting  the  precise  vibrations  im- 
parted to  it  without  any  alteration.  With  another  fork  a 
note  of  another  pitch  is  obtained.  Thus  fifty  forks  might 
be  employed  instead  of  two,  and  300  feet  of  wood  instead 
of  30;  the  rod  would  transmit  the  precise  vibrations  im- 
parted to  it,  and  no  other. 

We  are  now  prepared  to  appreciate  an  extremely  beau- 
tiful experiment,  for  which  we  are  indebted  to  Sir  Charles 
Wheatstone.  In  a  room  underneath  this,  and  separated 
from  it  by  two  floors,  is  a  piano.  Through  the  two  floors 
passes  a  tin  tube  2|  inches  in  diameter,  and  along  the 
axis  of  this  tube  passes  a  rod  of  deal,  the  end  of  which 
emerges  from  the  floor  in  front  of  the  lecture-table.  The 
rod  is  clasped  by  India-rubber  bands,  which  entirely  close 
the  tin  tube.  The  lower  end  of  the  rod  rests  upon  the 
sound-board  of  the  piano,  its  upper  end  being  exposed 
before  you.  An  artist  is  at  this  moment  engaged  at  the 
instrument,  but  you  hear  no  sound.  When,  however,  a 
violin  is  placed  upon  the  end  of  the  rod,  the  instrument 
becomes  instantly  musical,  not,  however,  with  the  vibra- 
tions of  its  own  strings,  but  with  those  of  the  piano.  When 
the  violin  is  removed,  the  sound  ceases;  putting  in  its 
place  a  guitar,  the  music  revives.  For  the  violin  and 
guitar  we  may  substitute  a  plain  wooden  tray,  which  is 
also  rendered  musical.  Here,  finally,  is  a  harp,  against  the 
sound-board  of  which  the  end  of  the  deal  rod  is  caused  to 
press;  every  note  of  the  piano  is  reproduced  before  you. 
On  lifting  the  harp  so  as  to  break  the  connection  with  the 


MUSICAL  SOUNDS  THEOUGH  SOLIDS.  109 

piano,  the  sound  vanishes;  but  the  moment  the  sound- 
board is  caused  to  press  upon  the  rod  the  music  is  restored. 
The  sound  of  the  piano  s6  far  resembles  that  of  the  harp 
that  it  is  hard  to  resist  the  impression  that  the  music  you 
hear  is  that  of  the  latter  instrument.  An  uneducated  per- 
son might  well  believe  that  witchcraft  or  "  spiritualism  " 
is  concerned  in  the  production  of  this  music. 

What  a  curious  transference  of  action  is  here  presented 
to  the  mind !  At  the  command  of  the  musician's  will,  the 
fingers  strike  the  keys;  the  hammers  strike  the  strings,  by 
which  the  rude  mechanical  shock  is  converted  into  tremors. 
The  vibrations  are  communicated  to  the  sound-board  of 
the  piano.  Upon  that  board  rests  the  end  of  the  deal  rod, 
thinned  off  to  a  sharp  edge  to  make  it  fit  more  easily  be- 
tween the  wires.  Through  the  edge,  and  afterward  along 
the  rod,  are  poured  with  unfailing  precision  the  entangled 
pulsations  produced  by  the  shocks  of  those  ten  agile  fin- 
gers. To  the  sound-board  of  the  harp  before  you,  the  rod 
faithfully  delivers  up  the  vibrations  of  which  it  is  the 
vehicle.  This  second  sound-board  transfers  the  motion  to 
the  air,  carving  it  and  chasing  it  into  forms  so  transcen- 
dently  complicated  that  confusion  alone  could  be  antici- 
pated from  the  shock  and  jostle  of  the  sonorous  waves. 
But  the  marvelous  human  ear  accepts  every  feature  of  the 
motion,  and  all  the  strife  and  struggle  and  confusion  melt 
finally  into  music  upon  the  brain.1 

1  An  ordinary  musical  box  may  be  substituted  for  the  piano  in  this 
experiment. 


HO  SOUND. 


SUMMARY  OF  CHAPTER  TL 

A  MUSICAL  sound  is  produced  by  sonorous  shocks 
which  follow  each  other  at  regular  intervals  with  a  suffi- 
cient rapidity  of  succession. 

Xoise  is  produced  by  an  irregular  succession  of  sonor- 
ous shocks. 

A  musical  sound  may  be  produced  by  taps  which  rap- 
idly and  regularly  succeed  each  other.  The  taps  of  a  card 
against  the  cogs  of  a  rotating  wheel  are  usually  employed 
to  illustrate  this  point. 

A  musical  sound  may  also  be  produced  by  a  succession 
of  puffs.  The  siren  is  an  instrument  by  which  such  puffs 
are  generated. 

The  pitch  of  a  musical  note  depends  solely  on  the 
number  of  vibrations  concerned  in  its  production.  The 
more  rapid  the  vibrations,  the  higher  the  pitch. 

By  means  of  the  siren  the  rate  of  vibration  of  any 
sounding  body  may  be  determined.  It  is  only  necessary 
to  render  the  sound  of  the  siren  and  that  of  the  body  iden- 
tical in  pitch  to  maintain  both  sounds  in  unison  for  a  cer- 
tain time,  and  to  ascertain,  by  means  of  the  counter  of  the 
siren,  how  many  puffs  have  issued  from  the  instrument  in 
that  time.  This  number  expresses  the  number  of  vibra- 
tions executed  by  the  sounding  body. 

When  a  body  capable  of  emitting  a  musical  sound — a 
tuning-fork,  for  example — vibrates,  it  moulds  the  sur- 
rounding air  into  sonorous  waves,  each  of  which  consists 
of  a  condensation  and  a  rarefaction. 

The  length  of  the  sonorous  wave  is  measured  from 


SUMMARY.  HI 

condensation  to  condensation,  or  from  rarefaction  to  rare- 
faction. 

The  wave-length  is  found  by  dividing  the  velocity  of 
sound  per  second  by  the  number  of  vibrations  executed  by 
the  sounding  body  in  a  second. 

Thus  a  tuning-fork  which  vibrates  256  times  in  a  sec- 
ond produces  in  air  of  15°  C.,  where  the  velocity  is  1,120 
feet  a  second,  waves  4  feet  4  inches  long.  While  two 
other  forks,  vibrating  respectively  320  and  384  times  a 
second,  generate  waves  3  feet  6  inches,  and  2  feet  11 
inches  long. 

A  vibration,  as  defined  in  England  and  Germany, 
comprises  a  motion  to  and  fro.  It  is  a  complete  vibration. 
In  France,  on  the  contrary,  a  vibration  comprises  a  move- 
ment to  or  fro.  The  French  vibrations  are  with  us  semi- 
vibrations. 

The  time  required  by  a  particle  of  air  over  which  a 
sonorous  wave  passes  to  execute  a  complete  vibration  is 
that  required  by  the  wave  to  move  through  a  distance 
equal  to  its  own  length. 

The  higher  the  temperature  of  the  air,  the  longer  is 
the  sonorous  wave  corresponding  to  any  particular  rate  of 
vibration.  Given  the  wave-length  and  the  rate  of  vibra- 
tion, we  can  readily  deduce  the  temperature  of  the 
air. 

The  human  ear  is  limited  in  its  range  of  hearing 
musical  sounds.  If  the  vibrations  number  less  than  16  a 
second,  we  are  conscious  only  of  the  separate  shocks.  If 
they  exceed  38,000  a  second,  the  consciousness  of  sound 
ceases  altogether.  The  range  of  the  best  ear  covers  about 
11  octaves,  but  an  auditory  range  limited  to  6  or  7  octaves 
is  not  uncommon. 

The  sounds  available  in  music  are  produced  by  vibra- 
tions comprised  between  the  limits  of  40  and  4,000  a 
second.  They  embrace  7  octaves. 


112  SOUND. 

The  range  of  the  ear  far  transcends  that  of  the  eye, 
which  hardly  exceeds  an  octave. 

By  means  of  the  Eustachian  tube,  which  is  opened  in 
the  act  of  swallowing,  the  pressure  of  the  air  on  both  sides 
of  the  tympanic  membrane  is  equalized. 

By  either  condensing  or  rarefying  the  air  behind  the 
tympanic  membrane,  deafness  to  sounds  of  low  pitch  may 
be  produced. 

On  the  approach  of  a  railway  train  the  pitch  of  the 
whistle  is  higher,  on  the  retreat  of  the  train  the  pitch  is 
lower,  than  it  would  be  if  the  train  were  at  rest. 

Musical  sounds  are  transmitted  by  liquids  and  solids. 
Such  sounds  may  be  transferred  from  one  room  to  an- 
other; from  the  ground-floor  to  the  garret  of  a  house  of 
many  stories,  for  example,  the  sound  being  unheard  in  the 
rooms  intervening  between  both,  and  rendered  audible 
only  when  the  vibrations  are  communicated  to  a  suitable 
sound-board. 


CHAPTER  III. 

Vibration  of  Strings.— How  employed  in  Music.— Influence  of  Sound- 
Boards. — Laws  of  Vibrating  Strings. — Combination  of  Direct  and 
Reflected  Pulses. — Stationary  and  Progressive  Waves. — Nodes  and 
Ventral  Segments.— Application  of  Results  to  the  Vibration  of 
Musical  Strings. — Experiments  of  Melde. — Strings  set  in  Vibration 
by  Tuning-Forks. — Laws  of  Vibration  thus  demonstrated. — Har- 
monic Tones  of  Strings.— Definitions  of  Timbre  or  Quality,  or 
Overtones  and  Clang. — Abolition  of  Special  Harmonics. — Condi- 
tions which  affect  the  Intensity  of  the  Harmonic  Tones. — Optical 
Examination  of  the  Vibrations  of  a  Piano-Wire. 

§  1.   Vibrations  of  Strings:  Use  of  Sound-Boards. 

WE  have  to  begin  our  studies  to-day  with  the  vibra- 
tions of  strings  or  wires;  to  learn  how  bodies  of  this  form 
are  rendered  available  as  sources  of  musical  sounds,  and 
to  investigate  the  laws  of  their  vibrations. 

To  enable  a  musical  string  to  vibrate  transversely,  or 
at  right  angles  to  its  length,  it  must  be  stretched  between 
two  rigid  points.  Before  you,  Fig.  31  (next  page),  is  an 
instrument  employed  to  stretch  strings,  and  to  render  their 
vibrations  audible.  From  the  pin  p,  to  which  one  end  of 
it  is  firmly  attached,  a  string  passes  across  the  two  bridges 
B  and  B',  being  afterward  carried  over  the  wheel  H,  which 
moves  with  great  freedom.  The  string  is  finally-stretched 
by  a  weight  w,  of  28  Ibs.,  attached  to  its  extremity.  The 
bridges  B  and  B',  which  constitute  the  real  ends  of  the 
string,  are  fastened  on  to  the  long1  wooden  box  M  N.  The 
whole  instrument  is  called  a  monochord,  or  sonometer. 

Taking  hold  of  the  stretched  string  B  B'  at  its  middle 

and  plucking  it  aside,  it  springs  back  to  its  first  position, 

passes  it,  returns,  and  thus  vibrates  for  a  time  to  and  fro 

across  its  position  of  equilibrium.    You  hear  a  sound,  but 

113 


114 


SOUND. 


the  sonorous  waves  which  at  present  strike  your  ears  do 
not  proceed  immediately  from  the  string.  The  amount 
of  wave-motion  generated  by  so  thin  a  body  is  too  small 
to  be  sensible  at  any  distance.  But  the  string  is  drawn 
tightly  over  the  two  bridges  B  B';  and  when  it  vibrates, 
its  tremors  are  communicated  through  these  bridges  to  the 
FIG.  31. 


entire  mass  of  the  box  M  N,  and  to  the  air  within  the  box, 
which  thus  become  the  real  sounding  bodies. 

That  the  vibrations  of  the  string  alone  are  not  sufficient 
to  produce  the  sound  may  be  thus  experimentally  demon- 
strated: A  B,  Fig.  32  (next  page),  is  a  piece  of  wood  placed 
across  an  iron  bracket  c.  From  each  end  of  the  piece  of 
wood  depends  a  rope  ending  in  a  loop,  while  stretching 
across  from  loop  to  loop  is  an  iron  bar  m  n.  From  the 
middle  of  the  iron  bar  hangs  a  steel  wire  s  s',  stretched  by 
a  weight  w,  of  28  Ibs.  By  this  arrangement  the  wire  is 
detached  from  all  large  surfaces  to  which  it  could  impart 
its  vibrations.  Plucking  the  wire  s  s',  it  vibrates  vigor- 
ously, but  even  those  nearest  to  it  do  not  hear  any  sound. 
The  agitation  imparted  to  the  air  is  too  inconsiderable 
to  affect  the  auditory  nerve  at  any  distance.  A  second 


INFLUENCE  OF  SOUND-BOARDS. 


115 


FIG.  32. 


wire  i  t',  Fig.  33  (next  page),  of  the  same  length,  thick- 
ness, and  material  as  s  s',  has  one  of  its  ends  attached  to 
the  wooden  tray  A  B.  This  wire  also  carries  a  weight  w, 
of  28  Ibs.  Finally,  passing 
over  the  bridges  B  B'  of  the 
sonometer,  Fig.  31,  is  our 
third  wire,  in  every  respect 
like  the  two  former,  and, 
like  them,  stretched  by  a 
weight  w,  of  28  Ibs.  When 
the  wire  i  t't  Fig.  33,  is 
caused  to  vibrate,  you  hear 
its  sound  distinctly.  Though 
one  end  only  of  the  wire  is 
connected  with  the  tray  A  B, 
the  vibrations  transmitted 
to  it  are  sufficient  to  con- 
vert the  tray  into  a  sound- 
ing body.  Finally,  when 
the  wire  of  the  sonometer 
M  N,  Fig.  31,  is  plucked,  the 
sound  is  loud  and  full,  be- 
cause the  instrument  is  spe- 
cially constructed  to  take 
up  the  variations  of  the 
wire. 

The  importance  of  em- 
ploying proper  sounding  ap- 
paratus in  stringed  instru- 
ments is  rendered  manifest 
by  these  experiments.  It  is 
not  the  strings  of  a  harp,  or  a  lute,  or  a  piano,  or  a  violin, 
that  throw  the  air  into  sonorous  vibrations.  It  is  the  large 
surfaces  with  which  the  strings  are  associated,  and  the  air 
inclosed  by  these  surfaces.  The  goodness  of  such  instru- 


116 


SOUND. 


ments  depends  almost  wholly  upon  the  quality  and  dis- 
position of  their  sound-boards.1 
Take  the  violin  as  an  example. 


FIG.  33. 


It  is,  or  ought  to  be, 
formed  of  wood 
of  the  most  per- 
fect elasticity. 
Imperfectly  elas- 
tic wood  expends 
the  motion  im- 
parted to  it  in 
the  friction  of  its 
own  molecules  ; 
the  motion  is  con- 
verted into  heat, 
instead  of  sound. 
The  strings  of  the 
violin  pass  from 
the  "  tail-piece  " 
of  the  instrument 
over  the  "bridge," 
being  thence  car- 
ried tothe"pegs," 
the  turning  of 
which  regulates 
the  tension  of 
the  strings.  The 
bow  is  drawn 
across  at  a  point 
about  one-tenth 
of  the  length  of  the  string  from  the  bridge.  The  two 

1  To  show  the  influence  of  a  large  vibrating  surface  in  communicat- 
ing sonorous  motion  to  the  air,  Mr.  Kilburn  incloses  a  musical  box 
within  cases  of  thick  felt.  Through  the  cases  a  wooden  rod,  which  rests 
upon  the  box,  issues.  When  the  box  plays  a  tune,  it  is  unheard  as  long 
as  the  rod  only  emerges ;  but  when  a  thin  disk  of  wood  is  fixed  on  the 
rod,  the  music  becomes  immediately  audible. 


INFLUENCE  OF  SOUND-BOARDS.  H7 

"  feet  "  of  the  bridge  rest  upon  the  most  yielding  portion 
of  the  "  belly  "  of  the  violin,  that  is,  the  portion  that  lies 
between  the  two  /-shaped  orifices.  One  foot  is  fixed  over 
a  short  rod,  the  "  sound  post,"  which  runs  from  belly  to 
back  through  the  interior  of  the  violin.  This  foot  of  the 
bridge  is  thereby  rendered  rigid,  and  it  is  mainly  through 
the  other  foot,  which  is  not  thus  supported,  that  the  vibra- 
tions are  conveyed  to  the  wood  of  the  instrument,  and 
thence  to  the  air  within  and  without.  The  sonorous  qual- 
ity of  the  wood  of  a  violin  is  mellowed  by  age.  The  very 
act  of  playing  also  has  a  beneficial  influence,  apparently 
constraining  the  molecules  of  the  wood,  which  in  the  first 
instance  might  be  refractory,  to  conform  at  last  to  the  re- 
quirements of  the  vibrating  strings. 

This  is  the  place  to  make  the  promised  reference  (page 
38)  to  Prof.  Stokes's  explanation  of  the  action  of  sound- 
boards. Although  the  amplitude  of  the  vibrating-board 
may  be  very  small,  still  its  larger  area  renders  the  abo- 
lition of  the  condensations  and  rarefactions  difficult.  The 
air  cannot  move  away  in  front  nor  slip  in  behind  be- 
fore it  is  sensibly  condensed  and  rarefied.  Hence  with 
such  vibrating  bodies  sound-waves  may  be  generated,  and 
loud  tones  produced,  while 
the  thin  strings  that  set 
them  in  vibration,  acting 
alone,  are  quite  inaudible. 

The  increase  of  sound, 
produced  by  the  stoppage 
of  lateral  motion,  has  been 
experimentally  illustrated 
by  Prof.  Stokes.  Let  the 
two  black  rectangles  in  Fig. 

34  represent  the  section  of  a  tuning-fork.  After  it  has 
been  made  to  vibrate,  place  a  sheet  of  paper,  or  the  blade 
of  a  broad  knife,  with  its  edge  parallel  to  the  axis  of  the 


118  SOUXD. 

fork,  and  as  near  to  the  fork  as  may  be  without  touching. 
If  the  obstacle  be  so  placed  that  the  section  of  it  is  A  or 
B  no  effect  is  produced;  but  if  it  be  placed  at  c,  so  as  to 
prevent  the  reciprocating  to-and-fro  movement  of  the  air, 
which  tends  to  abolish  the  condensations  and  rarefactions, 
the  sound  becomes  much  stronger. 

§  2.  Laws  of  Vibrating  Strings. 

Having  thus  learned  how  the  vibrations  of  strings  are 
rendered  available  in  music,  we  have  next  to  investigate 
the  laws  of  such  vibrations.  I  pluck  at  its  middle  point 
the  string  B  B',  Fig.  31.  The  sound  heard  is  the  funda- 
mental or  lowest  note  of  the  string,  to  produce  which  it 
swings,  as  a  whole,  to  and  fro.  By  placing  a  movable 
bridge  under  the  middle  of  the  string,  and  pressing  the 
string  against  the  bridge,  it  is  divided  into  two  equal 
parts.  Plucking  either  of  those  at  its  centre,  a  musical 
note  is  obtained,  which  many  of  you  recognize  as  the 
octave  of  the  fundamental  note.  In  all  cases,  and  with 
all  instruments,  the  octave  of  a  note  is  produced  by 
doubling  the  number  of  its  vibrations.  It  can,  moreover, 
be  proved,  both  by  theory  and  by  the  siren,  that  this  half 
string  vibrates  with  exactly  twice  the  rapidity  of  the 
whole.  In  the  same  way  it  can  be  proved  that  one-third 
of  the  string  vibrates  with  three  times  the  rapidity,  pro- 
ducing a  note  a  fifth  above  the  octave,  while  one-fourth  of 
the  string  vibrates  with  four  times  the  rapidity,  produc- 
ing the  double  octave  of  the  whole  string.  In  general 
terms,  the  number  of  vibrations  is  inversely  proportional 
to  the  length  of  the  string. 

Again,  the  more  tightly  a  string  is  stretched  the  more 
rapid  is  its  vibration.  When  this  comparatively  slack 
string  is  caused  to  vibrate,  you  hear  its  low  fundamental 
note.  By  turning  a  peg,  round  which  one  end  of  it  is 
coiled,  the  string  is  tightened,  and  the  pitch  rendered 


LAWS  OF  VIBRATING  STRINGS.  H9 

higher.  Taking  hold  with  my  left  hand  of  the  weight  w, 
attached  to  the  wire  B  B'  of  our  sonometer,  and  plucking 
the  wire  with  the  fingers  of  my  right,  I  alternately  press 
upon  the  weight  and  lift  it.  The  quick  variations  of  ten- 
sion are  expressed  by  a  varying  wailing  tone.  Xow,  the 
number  of  vibrations  executed  in  the  unit  of  time  bears  a 
definite  relation  to  the  stretching  force.  Applying  differ- 
ent weights  to  the  end  of  the  wire  B  B',  and  determining  in 
each  case  the  number  of  vibrations  executed  in  a  second, 
we  find  the  numbers  thus  obtained  to  be  proportional  to 
the  square  roots  of  the  stretching  weights.  A  string,  for 
example,  stretched  by  a  weight  of  one  pound,  executes  a 
certain  number  of  vibrations  per  second;  if 'we  wish  to 
double  this  number,  we  must  stretch  it  by  a  weight  of  four 
pounds;  if  we  wish  to  treble  the  number,  we  must  apply 
a  weight  of  nine  pounds,  and  so  on. 

The  vibrations  of  a  string  also  depend  upon  its  thick- 
ness. Preserving  the  stretching  weight,  the  length,  and 
the  material  of  the  string  constant,  the  number  of  vibra- 
tions varies  inversely  as  the  thickness  of  the  string.  If, 
therefore,  of  two  strings  of  the  same  material,  equally 
long  and  equally  stretched,  the  one  has  twice  the  diam- 
eter of  the  other,  the  thinner  string  will  execute  double 
the  number  of  vibrations  of  its  fellow  in  the  same  time. 
If  one  string  be  three  times  as  thick  as  another,  the  latter 
will  execute  three  times  the  number  of  vibrations,  and 
so  on. 

Finally,  the  vibrations  of  a  string  depend  upon  the 
density  of  the  matter  of  which  it  is  composed.  A  platinum 
wire  and  an  iron  wire,  for  example,  of  the  same  length 
and  thickness,  stretched  by  the  same  weight,  will  not  vi- 
brate with  the  same  rapidity.  For,  while  the  specific 
gravity  of  iron,  or  in  other  words  its  density,  is  7.8,  that 
of  platinum  is  21.5.  All  other  conditions  remaining  the 
same,  the  number  of  vibrations  is  inversely  proportional  to 


120  SOUND. 

the  square  root  of  the  density  of  the  string.  If  the  density 
of  one  string,  therefore,  be  one-fourth  that  of  another  of 
the  same  length,  thickness,  and  tension,  it  will  execute 
its  vibrations  twice  as  rapidly;  if  its  density  be  one-ninth 
that  of  the  other,  it  will  vibrate  with  three  times  the 
rapidity,  and  so  on.  The  two  last  laws,  taken  together, 
may  be  expressed  thus:  The  number  of  vibrations  is  in- 
versely proportional  to  the  square  root  of  the  weight  of 
the  string. 

In  the  violin  and  other  stringed  instruments  we  avail 
ourselves  of  thickness  instead  of  length  to  obtain  the 
deeper  tones.  In  the  piano  we  not  only  augment  the 
thickness  of  the  wires  intended  to  produce  the  bass  notes, 
but  we  load  them  by  coiling  round  them  an  extraneous 
substance.  They  resemble  horses  heavily  jockeyed,  and 
move  more  slowly  on  account  of  the  greater  weight  im- 
posed upon  the  force  of  tension. 

§  3.  Mechanical  Illustrations  of  Vibrations.  Progres- 
sive and  Stationary  Waves.  Ventral  Segments  and 
Nodes. 

These,  then,  are  the  four  laws  which  regulate  the 
transverse  vibrations  of  strings.  We  now  turn  to  certain 
allied  phenomena,  which,  though  they  involve  mechanical 
considerations  of  a  rather  complicated  kind,  may  be  com- 
pletely mastered  by  an  average  amount  of  attention.  And 
they  must  be  mastered  if  we  would  thoroughly  compre- 
hend the  philosophy  of  stringed  instruments. 

From  the  ceiling  c,  Fig.  35,  of  this  room  hangs  an 
India-rubber  tube  twenty-eight  feet  long.  The  tube  is 
filled  with  sand  to  render  its  motions  slow  and  more  easily 
followed  by  the  eye.  I  take  hold  of  its  free  end  a,  stretch 
the  tube  a  little,  and  by  properly  timing  my  impulses 
cause  it  to  swing  to  and  fro  as  a  whole,  as  shown  in  the 
figure.  It  has  its  definite  period  of  vibration  dependent 


STATIONARY  AND  PROGRESSIVE  WAVES. 


121 


FIG.  35. 


FIG.  30. 


1! 


on  its  length,  weight,  thickness,  and  tension,  and  my  im- 
pulses must  synchronize  with  that  period. 

I  now  stop  the  motion,  and  by  a  sudden  jerk  raise  a 
hump  upon  the  tube,  which  runs  along  it  as  a  pulse  toward 

its  fixed  end;  here  the  hump 

reverses  itself,  and  runs  back 

to  my  hand.    At  the  fixed  end 

of  the  tube,  in  obedience  to 

the  law  of  reflection,  the  pulse 

reversed  both  its  position  and 

the   direction   of   its   motion. 

Supposing  c,  Fig.  36,  to  be 

the  fixed  end  of  the  tube,  and 

a  the  end  held  in  the  hand :  if 

the  pulse  on  reaching  c  have 

the  position  shown  in  (1),  after 

reflection  it  will  have  the  posi- 
tion shown  in  (2).  The  arrows 

mark  the  direction  of  progres- 
sion.    The  time  required  for 

the   pulse   to   pass   from   the 

hand  to   the   fixed   end   and 

back  is  exactly  that  required 

to   accomplish   one   complete 

vibration    of   the    tube    as    a 

whole.     It  is  indeed  the  ad- 
dition of  such  impulses  which 

causes  the  tube   to   continue 

to  vibrate  as  a  whole. 

If,    instead    of    a    single 

jerk,  a  succession  of  jerks  be 

imparted,  thereby  sending  a 
series  of  pulses  along  the  tube,  every  one  of  them  will  be 
reflected  above,  and  we  have  now  to  inquire  how  the 
direct  and  reflected  pulses  behave  toward  each  other. 


122 


SOUXD. 


Let  the  time  required  by  Jthe  pulse  to  pass  from  my 
hand  to  the  fixed  end  be  one  second;  at  the  end  of  half  a 
second  it  occupies  the  position  a  b  (1),  Fig.  37,  its  fore- 
most point  having  reached  the  middle  of  the  tube.  At 
the  end  of  a  whole  second  it  would  have  the  position  b  c 
(2),  its  foremost  point  having 
reached  the  fixed  end  c  of  the 
tube.  At  the  moment  when  re- 
flection begins  at  c,  let  another 
jerk  be  imparted  at  a.  The 
reflected  pulse  from  c  moving 
with  the  same  velocity  as  this 
direct  one  from  a,  the  foremost 
points  of  both  will  arrive  at  the 
centre  b  (3)  at  the  same  moment. 
What  must  occur?  The  hump 
a  b  wishes  to  move  on  to  c,  and 
to  do  so  must  move  the  point 
6  to  the  right.  The  hump  c  b 
wishes  to  move  toward  a,  and 
to  do  so  must  move  the  point  b 
to  the  left.  The  point  6,  urged 
by  equal  forces  in  two  opposite 
directions  at  the  same  time,  will 
not  move  in  either  direction. 
Under  these  circumstances,  the 
two  halves  a  6,  b  c  of  the  tube 
will  oscillate  as  if  they  were  in- 
dependent of  each  other  (4). 
Thus  by  the  combination  of 
two  progressive  pulses,  the  one 
direct  and  the  other  reflected,  we  produce  two  stationary 
pulses  on  the  tube  a  c. 

The  vibrating  parts  a  b  and  b  c  are  called  ventral  seg- 
ments; the  point  of  no  vibration  b  is  called  a  node. 

The  term  "  pulse  "  is  here  used  advisedly,  instead  of 


NODES  AND  VENTRAL  SEGMENTS. 


123 


the  more  usual  term  wave.  For  a  wave  embraces  two  of 
these  pulses.  It  embraces  both  the  hump  and  the  de- 
pression which  follows  the  hump.  The  length  of  a  wave, 
therefore,  is  twice  that  of  a  ventral  segment. 

Supposing  the  jerks  to  be  so  timed  as  to  cause  each 

hump  to  be  one-third  of  the  tube's  length.    At  the  end  of 

one-third  of  a  second  from  starting  the  pulse  will  be  in 

the  position  a  &  (1),  Fig.  38.    In  two-thirds  of  a  second  it 

FIG.  38. 


i 
I 

|\ 

1 

A 

1 

! 

5' 
I 

(  1 

• 

.  "  1 
b 

6 

!  I 

a 

i 

3                     < 

i 

a             a 

V 

a 

0)  (2)  (3)  (4)  (6)  (6)  (T) 

will  have  reached  the  position  &  &'  (2),  Fig.  38.    At  this 
moment  let  a  new  pulse  be  started  at  a;  after  the  lapse  of 


124:  SOUND. 

an  entire  second  from  the  commencement  we  shall  have 
two  humps  upon  the  tube,  one  occupying  the  position 
a  b  (3),  the  other  the  position  V  c  (3).  It  is  here  manifest 
that  the  end  of  the  reflected  pulse  from  c,  and  the  end  of 
the  direct  one  from  a,  will  reach  the  point  b'  at  the  same 
moment.  We  shall  therefore  have  the  state  of  things  rep- 
resented in  (4),  where  b  V  wishes  to  move  upward,  and 
c  br  to  move  downward.  The  action  of  both  upon  the 
point  b'  being  in  opposite  directions,  that  point  will  re- 
main fixed.  And  from  it,  as  if  it  were  a  fixed  point,  the 
pulse  b  b'  will  be  reflected,  while  the  segment  b'  c  will 
oscillate  as  an  independent  string.  Supposing  that  at 
the  moment  b  V  (4)  begins  to  be  reflected  at  b'  we  start 
another  pulse  from  a,  it  will  reach  b  at  the  same  moment 
the  pulse  reflected  from  b'  reaches  it.  The  pulses  will 
neutralize  each  other  at  b,  and  we  shall  have  there  a  sec- 
ond node.  Thus,  by  properly  timing  our  jerks,  we  divide 
the  rope  into  three  ventral  segments,  separated  from  each 
other  by  two  nodal  points.  As  long  as  the  agitation  con- 
tinues the  tube  will  vibrate  as  in  (6). 

There  is  no  theoretic  limit  to  the  number  of  nodes 
and  ventral  segments  that  may  be  thus  produced.  By  the 
quickening  of  the  impulses,  the  tube  is  divided  into  four 
ventral  segments  separated  by  three  nodes;  quickening 
still  more  we  have  five  ventral  segments  and  four  nodes. 
With  this  particular  tube  the  hand  may  be  caused  to 
vibrate  sufficiently  quick  to  produce  ten  ventral  segments, 
as  shown  in  Fig.  38  (7).  When  the  stretching  force  is 
constant,  the  number  of  ventral  segments  is  proportional 
to  the  rapidity  of  the  hand's  vibration.  To  produce 
2,  3,  4,  10  ventral  segments  requires  twice,  three  times, 
four  times,  ten  times  the  rapidity  of  vibration  necessary 
to  make  the  tube  swing  as  a  whole.  When  the  vibration 
is  very  rapid  the  ventral  segments  appear  like  a  series 
of  shadowy  spindles,  separated  from  each  other  by  dark 


STATIONARY  WAVES.  125 

motionless  nodes.    The  experiment  is  a  beautiful  one,  and 
it  is  easily  performed. 

If,  instead  of  moving  the  hand  to  and  fro,  it  be  caused 
to  describe  a  small  circle,  the  ventral  segments  become 
"  surfaces  of  revolution."  Instead  of  the  hand,  moreover, 
we  may  employ  a  hook  turned  by  a  whirling-table.  Before 
you  is  a  cord  more  rigid  than  the  India-rubber  tube,  25 
feet  long,  with  one  of  its  ends  attached  to  a  freely-moving 
swivel  fixed  in  the  ceiling  of  the  room.  By  turning  the 
whirling-table  to  which  the  other  end  is  attached,  this 
cord  may  be  divided  into  as  many  as  20  ventral  segments, 
separated  from  each  other  by  their  appropriate  nodes.  In 
another  arrangement  a  string  of  catgut  12  feet  long, 
with  silvered  beads  strung  along  it,  is  stretched  horizon- 
tally between  a  vertical  wheel  and  a  free  swivel  fixed  in  a 
rigid  stand.  On  turning  the  wheel,  and  properly  regu- 
lating both  the  tension  and  the  rapidity  of  rotation,  the 
beaded  cord  may  be  caused  to  .rotate  as  a  whole,  and  to 
divide  itself  successively  into  2,  3,  4,  or  5  ventral  seg- 
ments. When  we  envelop  the  cord  in  a  luminous  beam, 
every  spot  of  light  on  every  bead  describes  a  brilliant  cir- 
cle, and  a  very  beautiful  experiment  is  the  result. 

§  4.  Mechanical  Illustrations  of  Damping  Various 
Points  of  Vibrating  Cord. 

The  subject  of  stationary  waves  was  first  experimen- 
tally treated  by  the  Messrs.  Weber,  in  their  excellent  re- 
searches on  wave-motion.  It  is  a  subject  which  will  well 
repay  your  attention  by  rendering  many  of  the  most  diffi- 
cult phenomena  of  musical  strings  perfectly  intelligible. 
It  will  make  the  connection  of  both  classes  of  vibrations 
more  obvious  if  we  vary  our  last  experiments.  Before  you 
is  a  piece  of  India-rubber  tubing,  10  or  12  feet  long, 
stretched  from  c  to  a,  Fig.  39,  and  made  fast  to  two  pins 
at  c  and  a.  The  tube  is  blackened,  and  behind  it  is 


126 


SOUND. 


placed  a  surface  of  white  paper,  to  render  its  motions 
more  visible.  Encircling  the  tube  at  its  centre  6  (1)  by 
the  thumb  and  forefinger  of  my  left  hand,  and  taking 
the  middle  of  the  lower  half  &  a  of  the  tube  in  my  right, 
I  pluck  it  aside.  Not  only  does  the  lower  half  swing,  but 
FIG.  39. 


1 

A 

e 

e 

1 

e 

1 

i 

I 

1 

1 

\ 

I 

I 

i  ' 

\  7 

1 

j 

^ 

b 

s 

j 

I 

1 

| 

c 

-^ 

-t^ 

j 

1 

w 

\7 

| 

(1)  (2)  (3)  (4)  (5)  (6) 

the  upper  half  also  is  thrown  into  vibration.  Withdraw- 
ing the  hands  wholly  from  the  tube,  its  two  halves  a  & 
and  6  c  continue  to  vibrate,  being  separated  from  each 
other  by  a  node  &  at  the  centre  (2). 

I  now  encircle  the  tube  at  a  point  &  (3)  one-third  of 


THE  NODES  NOT  POINTS  OF  ABSOLUTE  REST.    127 

its  length  from  its  lower  end  a,  and,  taking  hold  of  a  &  at 
its  centre,  pluck  it  aside;  the  length  b  c  above  my  hand 
instantly  divides  into  two  vibrating  segments.  With- 
drawing the  hands  wholly,  you  see  the  entire  tube  divided 
into  three  ventral  segments,  separated  from  each  other  by 
two  motionless  nodes,  b  and  V  (4).  I  pass  on  to  the  point 
b  (5),  which  marks  off  one-fourth  of  the  length  of  the 
tube,  encircle  it,  and  pluck  the  shorter  segment  aside. 
The  longer  segment  above  my  hand  divides  itself  imme- 
diately into  three  vibrating  parts.  So  that,  on  withdraw- 
ing the  hand,  the  whole  tube  appears  before  you  divided 
into  four  ventral  segments,  separated  from  each  other  by 
three  nodes  6  &'  &"  (6).  In  precisely  the  same  way  the 
tube  may  be  divided  into  five  vibrating  segments  with 
four  nodes. 

This  sudden  division  of  the  long  upper  segment  of  the 
tube,  without  any  apparent  cause,  is  very  surprising;  but 
if  you  grant  me  your  attention  for  a  moment,  you  will  find 
that  these  experiments  are  essentially  similar  to  those 
which  illustrated  the  coalescence  of  direct  and  reflected 
undulations.  Reverting  for  a  moment  to  the  latter,  you 
observed  that  the  to-and-fro  motion  of  the  hand  through 
the  space  of  a  single  inch  was  sufficient  to  make  the 
middle  points  of  the  ventral  segments  vibrate  through  a 
foot  or  eighteen  inches.  By  being  properly  timed  the 
impulses  accumulated,  until  the  amplitude  of  the  vibrat- 
ing segments  exceeded  immensely  that  of  the  hand  which 
produced  them.  The  hand,  in  fact,  constituted  a  nodal 
point,  so  small  was  its  comparative  motion.  Indeed,  it  is 
usual,  and  correct,  to  regard  the  ends  of  the  tube  also  as 
nodal  points. 

Consider  now  the  case  represented  in  (1),  Fig.  39, 
where  the  tube  was  encircled  at  its  middle,  the  lower  seg- 
ment a  b  being  thrown  into  the  vibration  corresponding 
to  its  length  and  tension.  The  circle  formed  by  the  finger 


128  SOUND. 

and  thumb  permitted  the  tube  to  oscillate  at  the  point  b 
through  the  space  of  an  inch;  and  the  vibrations  at  that 
point  acted  upon  the  upper  half  b  c  exactly  as  my  hand 
acted  when  it  caused  the  tube  suspended  from  the  ceiling 
to  swing  as  a  whole,  as  in  Fig.  35.  Instead  of  the  timid 
vibrations  of  the  hand,  we  have  now  the  timid  vibrations 
of  the  lower  half  of  the  tube ;  and  these,  though  narrowed 
to  an  inch  at  the  place  clasped  by  the  finger  and  thumb, 
soon  accumulate,  and  finally  produce  an  amplitude,  in  the 
upper  half,  far  exceeding  their  own.  The  same  reasoning 
applies  to  all  the  other  cases  of  subdivision.  If,  instead 
of  encircling  a  point  by  the  finger  and  thumb,  and  pluck- 
ing the  portion  of  the  tube  below  it  aside,  that  same  point 
were  taken  hold  of  by  the  hand  and  agitated  in  the  period 
proper  to  the  lower  segment  of  the  tube,  precisely  the 
same  effect  would  -be  produced.  We  thus  reduce  both 
effects  to  one  and  the  same  cause;  namely,  the  combina- 
tion of  direct  and  reflected  undulations. 

And  here  let  me  add  that,  when  the  tube  was  divided 
by  the  timid  impulses  of  the  hand,  not  one  of  its  nodes 
was,  strictly  speaking,  a  point  of  no  motion;  for  were  the 
nodes  not  capable  of  vibrating  through  a  very  small  ampli- 
tude, the  motion  of  the  various  segments  of  the  tube  could 
not  be  maintained. 

§  5.  Stationary  Water-waves. 

What  is  true  of  the  undulations  of  an  India-rubber 
tube  applies  to  all  undulations  whatsoever.  Water-waves, 
for  example,  obey  the  same  laws,  and  the  coalescence 
of  direct  and  reflected  waves  exhibits  similar  phenomena. 
This  long  and  narrow  vessel  with  glass  sides,  Fig.  40,  is  a 
copy  of  the  wave-canal  of  the  brothers  Weber.  It  is  filled 
to  the  level  A  B  with  colored  water.  By  tilting  the  end  A 
suddenly,  a  wave  is  generated,  which  moves  on  to  B,  and 
is  there  reflected.  By  sending  forth  fresh  waves  at  the 


STATIONARY  WATER-WAVES.  129 

proper  intervals,  the  surface  is  divided  into  two  stationary 
undulations.  Making  the  succession  of  impulses  more 
rapid  we  can  subdivide  the  surface  into  three,  four  (shown 
in  the  figure),  or  more  stationary  undulations,  separated 
from  each  other  by  nodes.  The  step  of  a  water-carrier  is 
sometimes  so  timed  as  to  throw  the  surface  of  the  water  in 
his  vessel  into  stationary  waves,  which  may  augment  ill 
height  until  the  water  splashes  over  the  brim.  Practice 
has  taught  the  water-carrier  what  to  do;  he  changes  his 
step,  alters  the  period  of  his  impulses,  and  thus  stops  the 
accumulation  of  the  motion. 

In  traveling  recently  in  the  coupe  of  a  French  railway 
carriage,  I  had  occasion  to  place  a  bottle  half  filled  with 
water  on  one  of  the  little  coupe  tables.  It  was  interesting 

FIG.  40. 


to  observe  it.  At  times  it  would  be  quite  still;  at  times 
it  would  oscillate  violently.  To  the  passenger  within  the 
carriage  there  was  no  sensible  change  in  the  motion  of  the 
train  to.  which  the  difference  could  be  ascribed.  But  in 
the  one  case  the  tremor  of  the  carriage  contained  no  vibra- 
tions synchronous  with  the  oscillating  period  of  the  water, 
while  in  the  other  case  such  vibrations  were  present.  Out 
of  the  confused  assemblage  of  tremors  the  water  selected 
the  particular  constituent  which  belonged  to  itself,  and 
declared  its  presence  when  the  traveler  was  utterly  un- 
conscious of  its  introduction. 


130  SOUND. 

§  6.  Application  of  Mechanical  Illustrations  to  Musical 
Strings. 

From  these  comparatively  gross,  but  by  no  means  un- 
beautiful,  mechanical  vibrations,  we  pass  to  those  of  a 
sounding  string.  In  the  experiments  with  our  monochord, 
when  the  wire  was  to  be  shortened,  a  movable  bridge  was 
employed,  against  which  the  wire  was  pressed  so  as  to 
deprive  the  point  resting  on  the  bridge  of  all  possibility 
of  motion.  This  strong  pressure,  however,  is  not  neces- 
sary. Placing  the  feather-end  of  a  goose-quill  lightly 
against  the  middle  of  the  string,  and  drawing  a  violin-bow 
over  one  of  its  halves,  the  string  yields  the  octave  of  the 
note  yielded  by  the  whole  string.  The  mere  damping  of 
the  string  at  the  centre,  by  the  light  touch  of  the  feather, 
is  sufficient  to  cause  the  string  to  divide  into  two  vibrating 
segments.  Nor  is  it  necessary  to  hold  the  feather  there 
throughout  the  experiment:  after  having  drawn  the  bow, 
the  feather  may  be  removed;  the  string  will  continue  to 
vibrate,  emitting  the  same  note  as  before.  We  have  here 
a  case  exactly  analogous  to  that  in  which  the  central  point 
of  our  stretched  India-rubber  tube  was  damped,  by  encir- 
cling it  with  the  finger  and  thumb  as  in  Fig.  39  (1).  Not 
only  did  the  half  plucked  aside  vibrate,  but  the  other  half 
vibrated  also.  We  can,  in  fact,  reproduce,  with  the  vi- 
brating string,  every  effect  obtained  with  the  tube.  This, 
however,  is  a  point  of  such  importance  as  to  demand  full 
experimental  illustration. 

To  prove  that  when  the  centre  is  damped,  and  the  bow 
drawn  across  one  of  the  halves  of  the  string,  the  other 
half  vibrates,  I  place  across  the  middle  of  the  untouched 
half  a  little  rider  of  red  paper.  Damping  the  centre  and 
drawing  the  bow,  the  string  shivers,  and  the  rider  is  over- 
thrown, Fig.  41. 

When  the  string  is  damped  at  a  point  which  cuts  off 


DIVISION  OF  MUSICAL  STRINGS. 


131 


one-third  of  its  length,  and  the  bow  drawn  across  the 
shorter  section,  not  only  is  this  section  thereby  thrown 
into  vibration,  but  the  longer  section  divides  itself  into 
two  ventral  segments  with  a  node  between  them.  This  is 
proved  by  placing  small  riders  of  red  paper  on  the  ventral 


segments,  and  a  rider  of  blue  paper  at  the  node.  Passing 
the  bow  across  the  short  segment  you  observe  a  fluttering 
of  the  red  riders,  and  now  they  are  completely  tossed  off, 
while  the  blue  rider  which  crosses  the  node  is  undisturbed, 
Fig.  42. 

Damping  the  string  at  the  end  of  one-fourth  of  its 


length,  the  bow  is  drawn  across  the  shorter  section;  the 
remaining  three-fourths  divide  themsjelves  into  three  ven- 


132 


SOUND. 


tral  segments,  with  two  nodes  between  them.  This  is 
proved  by  the  unhorsing  of  the  three  riders  placed  astride 
the  ventral  segments,  the  two  at  the  nodes  keeping  their 
places  undisturbed,  Fig.  43. 

Finally,  damping  the  string  at  the  end  of  one-fifth  of 

FIG.  43.  (f 


its  length,  and  arranging,  as  before,  the  red  riders  on  the 
ventral  segments  and  the  blue  ones  on  the  nodes,  by  a 
single  sweep  of  the  bow  the  four  red  riders  are  unhorsed, 
and  the  three  blue  ones  left  undisturbed,  Fig.  44.  In  this 
way  we  perform  with  a  sounding  string  the  same  series  of 


experiments  that  were  formerly  executed  with  a  stretched 
India-rubber  tube,  the  results  in  both  cases  being  iden- 
tical.1 

1  Chladni  remarks  ("  Akustik,"  p.  55)  that  it  is  usual  to  ascribe  to 
Sauveur  the  discovery,  in  1701,  of  the  nodes  of  vibration  corresponding  to 


MELDE'S  EXPERIMENTS.  133 

To  make,  if  possible,  this  identity  still  more  evident  to 
you,  a  stout  steel  wire  28  feet  in  length  is  stretched 
behind  the  table  from  side  to  side  of  the  room.  I  take 
the  central  point  of  this  wire  between  my  finger  and 
thumb,  and  allow  my  assistant  to  pluck  one-half  of  it 
aside.  It  vibrates,  and  the  vibrations  transmitted  to  the 
other  half  are  sufficiently  powerful  to  toss  into  the  air  a 
large  sheet  of  paper  placed  astride  the  wire.  "With  this 
long  wire,  and  with  riders  not  of  one-eighth  of  a  square 
inch,  but  of  30,  40,  or  50  square  inches  in  area,  we  may 
repeat  all  the  experiments  which  you  have  witnessed  with 
the  musical  string.  The  sheets  of  paper  placed  across  the 
nodes  remain  always  in  their  places,  while  those  placed 
astride  the  ventral  segments  are  tossed  simultaneously  into 
the  air  when  the  shorter  segment  of  the  wire  is  set  in  vi- 
bration. In  this  case,  when  close  to  it,  you  can  actually 
see  the  division  of  the  wire. 

§  7.  Melde's  Experiments. 

It  is  now  time  to  introduce  to  your  notice  some  recent 
experiments  on  vibrating  strings,  which  appeal  to  the  eye 
with  a  beauty  and  a  delicacy  far  surpassing  anything 
attainable  with  our  monochord.  To  M.  Melde,  of  Mar- 
burg, we  are  indebted  for  this  new  method  of  exhibiting 
the  vibrations  of  strings.  The  scale  of  the  experiments 
will  be  here  modified  so  as  to  suit  our  circumstances. 

First,  then,  you  observe  here  a  large  tuning-fork  T, 
Fig.  45,  with  a  small  screw  fixed  into  the  top  of  one  of  its 
prongs,  by  which  a  silk  string  can  be  firmly  attached  to 
the  prong.  From  the  fork  the  string  passes  round  a  dis- 
tant peg  P,  by  turning  which  it  may  be  stretched  to  any 
required  extent.  When  the  bow  is  drawn  across  the  fork, 
an  irregular  flutter  of  the  string  is  the  only  result.  On 
the  higher  tones  of  strings ;  but  that  Noble  and  Pigott  had  made  the  dis- 
covery in  Oxford  in  1676,  and  that  Sauveur  declined  the  honor  of  the  dis- 
covery when  he  found  that  others  had  made  the  observation  before  him. 


134  SOUND. 

tightening  it,  however,  when  at  the  proper  tension  it 
expands  into  a  beautiful  gauzy  spindle  six  feet  long,  more 
than  six  inches  across  at  its  widest  part,  and  shining  with 
a  kind  of  pearly  lustre.  The  stretching  force  at  the  pres- 
ent moment  is  such  that  the  string  swings  to  and  fro  as  a 
whole,  its  vibrations  being  executed  in  a  vertical  plane. 

Relaxing  the  string  gradually,  when  the  proper  tension 
has  been  reached,  it  suddenly  divides  into  two  ventral 
segments,  separated  from  each  other  by  a  sharply-defined 
and  apparently  motionless  node. 

AVhile  the  fork  continues  vibrating,  if  the  string  be 

FIG.  45. 


relaxed  still  further,  it  divides  into  three  vibrating  parts. 
Slackening  it  still  more,  it  divides  into  four  vibrating 
parts.  And  thus  we  might  continue  to  subdivide  the  string 
into  ten,  or  even  twenty  ventral  segments,  separated  from 
each  other  by  the  appropriate  number  of  nodes. 

When  white-silk  strings  vibrate  thus,  the  nodes  appear 
perfectly  fixed,  while  the  ventral  segments  form  spindles 
of  the  most  delicate  beauty.  Every  protuberance  of  the 
twisted  string,  moreover,  writes  its  motion  in  a  more  or 
less  luminous  line  on  the  surface  of  the  aerial  gauze. 
The  four  nodes  of  vibration  just  illustrated  are  represented 
in  Fig.  46  (next  page),  1,  2,  3,  4.1 

1  The  first  experiment  really  made  in  the  lecture  was  with  a  bar  of 
steel  62  inches  long,  1|  inch  wide,  and  |  an  inch  thick,  bent  into  the 


STRINGS  EXCITED  BY  TUNING-FORKS.  135 

When  the  synchronism  between  fork  and  string  is 
perfect,  the  vibrations  of  the  string  are  steady  and  long- 
continued.     A  slight  departure  from  synchronism,  how- 
ever, introduces  unsteadiness,  and  the  ventral  segments, 
FIG.  46. 


though  they  may  show  themselves  for  a  time,  quickly 
disappear. 

In  the  experiments  just  executed  the  fork  vibrated  in 

shape  of  a  tuning-fork,  with  its  prongs  2  inches  apart,  and  supported  on 
a  heavy  stand.  The  cord  attached  to  it  was  9  feet  long  and  a  quarter  of 
an  inch  thick.  The  pronsrs  were  thrown  into  vibration  by  striking  them 
briskly  with  two  pieces  of  lead  covered  with  pads  and  held  one  in  each 
hand.  The  prongs  vibrated  transversely  to  the  cord.  The  vibrations 
produced  by  a  single  stroke  were  sufficient  to  carry  the  cord  through 
several  of  its  subdivisions  and  back  to  a  single  ventral  segment.  That 
is  to  say,  by  striking  the  prongs  and  causing  the  cord  to  vibrate  as  a 
whole,  it  could,  by  relaxing  the  tension,  be  caused  to  divide  into  two, 
three,  or  four  vibrating  segments ;  and  then,  by  increasing  the  tension, 
to  pass  back  through  four,  three,  and  two  divisions,  to  one,  without  re- 
newing the  agitation  of  Me  prongs.  The  cord  was  of  such  a  character 
that,  instead  of  oscillating  to  and  fro  in  the  same  plane,  each  of  its 
points  described  a  circle.  The  ventral  segments,  therefore,  instead  of 
being  flat  surfaces  were  surfaces  of  revolution,  and  were  equally  well 
seen  from  all  parts  of  the  room.  The  tuning-forks  employed  in  the 
subsequent  illustrations  were  prepared  for  me  by  that  excellent  acoustic 
mechanician,  Konisr,  of  Paris,  being  such  as  are  usually  employed  in 
the  projection  of  Lissajou's  experiments. 


136  SOUND. 

the  direction  of  the  length  of  the  string.  Every  forward 
stroke  of  the  fork  raised  a  protuberance,  which  ran  to  the 
fixed  end  of  the  string,  and  was  there  reflected;  so  that 
when  the  longitudinal  impulses  were  properly  timed  they 
produced  a  transverse  vibration.  Let  us  consider  this 
further.  One  end  of  this  heavy  cord  is  attached  to  a 
hook  A,  Fig.  47,  fixed  in  the  wall.  Laying  hold  of  the 
other  end  I  stretch  the  cord  horizontally,  and  then  move 
my  hand  to  and  fro  in  the  direction  of  the  cord.  It  swings 
as  a  whole,  and  you  may  notice  that  always,  when  the  cord 
is  at  the  limit  of  its  swing,  the  hand  is  in  its  most  forward 
position.  If  it  vibrate  in  a  vertical  plane,  the  hand,  in 
order  to  time  the  impulses  properly,  must  be  at  its  for- 
ward limit  at  the  moment  the  cord  reaches  the  upper 
FIG.  47. 


boundary,  and  also  at  the  moment  it  reaches  the  lower 
boundary  of  its  excursion.  A  little  reflection  will  make  it 
plain  that,  in  order  to  accomplish  this,  the  hand  must 
execute  a  complete  vibration  while  the  cord  executes  a 
semi- vibration ;  in  other  words,  the  vibrations  of  the  hand 
must  be  twice  as  rapid  as  those  of  the  cord. 

Precisely  the  same  is  true  of  our  tuning-fork.  When 
the  fork  vibrates  in  the  direction  of  the  string,  the  number 
of  vibrations  which  it  executes  in  a  certain  time  is  twice 
the  number  executed  by  the  string  itself.  And  if,  while 
arranged  thus,  a  fork  and  string  vibrate  with  sufficient 
rapidity  to  produce  musical  notes,  the  note  of  the  fork 
will  be  an  octave  above  that  of  the  string. 

But  if,  instead  of  the  hand  being  moved  to  and  fro  in 
the  direction  of  this  heavy  cord,  it  is  moved  at  right  angles 


STRINGS  EXCITED  BY  TUNING-FORKS.  137 

to  that  direction,  then  every  upward  movement  of  the 
hand  coincides  with  an  upward  movement  of  the.  cord; 
every  downward  movement  of  the  hand  with  a  downward 
movement  of  the  cord.  In  fact,  the  vibrations  of  hand 
and  string,  in  this  case,  synchronize  perfectly;  and  if  the 
hand  could  emit  a  musical  note,  the  cord  would  emit  a 
note  of  the  same  pitch.  The  same  holds  good  when  a  vi- 
brating fork  is  substituted  for  the  vibrating  hand. 

Hence,  if  the  string  vibrate  as  a  whole  when  the  vibra- 
tions of  the  fork  are  along  it,  it  will  divide  into  two  ven- 
tral segments  wherf  the  vibrations  are  across  it;  or,  more 
generally  expressed,  preserving  the  tension  constant,  what- 
ever be  the  number  of  ventral  segments  produced  by  the 
fork  when  its  vibrations  are  in  the  direction  of  the  string, 
twice  that  number  will  be  produced  when  the  vibrations 
are  transverse  to  the  string.  The  string  A  B,  for  example, 
Figs.  48  and  49,  passing  over  a  pulley  B,  is  stretched  by  a 
definite  weight  (not  shown  in  the  figure).  When  the  tun- 
ing-fork vibrates  along  it,  as  in  Fig.  48,  the  string  divides 

FIG.  48. 


into  two  equal  ventral  segments.  When  the  fork  is  turned 
so  that  it  shall  vibrate  at  right  angles  to  the  string,  the 
number  of  ventral  segments  is  four,  Fig.  49,  or  double  the 

FIG.  49. 


former  number.  Attaching  two  strings  of  the  same  length 


138.  SOUND. 

to  the  same  fork,  the  one  parallel  and  the  other  perpendic- 
ular to  the  direction  of  vibration,  and  stretching  both  with 
equal  weights,  when  the  fork  is  caused  to  vibrate,  one  of 
them  divides  itself  into  twice  the  number  of  ventral  seg- 
ments exhibited  by  the  other. 

A  number  of  exquisite  effects  may  be  obtained  with 
these  vibrating  cords.  The  path  described  by  any  point 
of  any  one  of  them  may  be  studied,  after  the  manner  of 
Dr.  Young,  by  illuminating  that  point,  and  watching  the 
line  of  light  which  it  describes.  This  is  well  illustrated  by 
a  flat  burnished  silver  wire,  twisted  so  as  to  form  a  spiral 
surface,  from  which,  at  regular  intervals,  the  light  flashes 
when  the  wire  is  illuminated.  When  the  vibration  is 
steady,  the  luminous  spots  describe  straight  lines  of  sun- 
like  brilliancy.  On  slackening  the  wire,  but  not  so  much 
as  to  produce  its  next  higher  subdivision,  upon  the  larger 
motion  of  the  wire  are  superposed  a  host  of  minor  motions, 
the  combination  of  all  producing  scrolls  of  marvelous 
complication  and  of  indescribable  splendor. 

In  reflecting  on  the  best  means  of  rendering  these 
effects  visible,  the  thought  occurred  to  me  of  employing  a 
fine  plantinum  wire  heated  to  redness  by  an  electric  cur- 
rent. Such  a  wire  now  stretches  from  a  tuning-fork  over 
a  bridge  of  copper,  and  then  passes  round  a  peg.  The 
copper  bridge  on  the  one  hand  and  the  tuning-fork  on  the 
other  are  the  poles  of  a  voltaic  battery,  from  which  a  cur- 
rent passes  through  the  wire  and  causes  it  to  glow.  On 
drawing  the  bow  across  the  fork,  the  wire  vibrates  as  a 
whole;  its  two  ends  are  brilliant,  while  its  middle  is  dark, 
being  chilled  by  its  rapid  passage  through  the  air.  Thus 
you  have  a  shading  off  of  incandescence  from  the  ends  to 
the  centre  of  the  wire.  On  relaxing  the  tension,  the  wire 
divides  itself  into  two  ventral  segments;  on  relaxing  still 
further,  we  obtain  three;  still  further,  and  the  wire  di- 
vides into  four  ventral  segments,  separated  from  each 


NEW  DETERMINATION  OF  LAWS  OF  VIBRATION.   139 

other  by  three  brilliant  nodes.  Right  and  left  from  every 
node  the  incandescence  shades  away  until  it  disappears. 
You  notice  also,  when  the  wire  settles  into  steady  vibra- 
tion, that  the  nodes  shine  out  with  greater  brilliancy  than 
that  possessed  by  the  wire  before  the  vibration  com- 
menced. The  reason  is  this.  Electricity  passes  more 
freely  along  a  cold  wire  than  along  a  hot  one.  When, 
therefore,  the  vibrating  segments  are  chilled  by  their  swift 
passage  through  the  air,  their  conductivity  is  improved, 
more  electricity  passes  through  the  vibrating  than  through 
the  motionless  wire,  and  hence  the  augmented  glow  of  the 
nodes.  If,  previous  to  the  agitation  of  the  fork,  the  wire 
be  at  a  bright-red  heat,  when  it  vibrates  its  nodes  may  be 
raised  to  the  temperature  of  fusion. 

§  8.  New  Mode  of  determining  the  Laws  of  Vibration. 

"We  may  extend  the  experiments  of  M.  Melde  to  the 
establishment  of  all  the  laws  of  vibrating  strings.  Here 
are  four  tuning-forks,  which  we  may  call  a,  &,  c,  d,  whose 
rates  of  vibration  are  to  each  other  as  the  numbers  1,  2, 
4,  8.  To  the  largest  fork  is  attached  a  string,  a,  stretched 
by  a  weight,  which  causes  it  to  vibrate  as  a  whole.  Keep- 
ing the  stretching  weight  the  same,  I  determine  the 
lengths  of  the  same  string,  which,  when  attached  to  the 
other  three  forks,  &,  c,  d,  swing  as  a  whole.  The  lengths  in 
the  four  respective  cases  are  as  the  numbers  8,  4,  2,  1. 

From  this  follows  the  first  law  of  vibration,  already 
established  (p.  118)  by  another  method,  viz.:  the  length 
of  the  string  is  inversely  proportional  to  the  rapidity  of 
vibration.1 

In  this  case  the  longest  string  vibrates  as  a  whole  when 

1  A  string  steeped  in  a  solution  of  the  sulphate  of  quinine,  and  illu- 
minated by  the  violet  rays  of  the  electric  lamp,  exhibits  brilliant  fluores- 
cence. When  the  fork  to  which  it  is  attached  vibrates,  the  string  divides 
itself  into  a  series  of  spindles,  and  separated  from  each  other  by  more  in- 
tensely luminous  nodes,  emitting  a  light  of  the  most  delicate  greenish-blue. 


140  SOUND. 

attached  to  the  fork  a.  I  now  transfer  the  string  to  b,  still 
keeping  it  stretched  by  the  same  weight.  It  vibrates  when 
b  vibrates;  but  how?  By  dividing  into  two  equal  ventral 
segments.  In  this  way  alone  can  it  accommodate  itself  to 
the  swifter  vibrating  period  of  b.  Attached  to  c,  the 
same  string  separates  into  four,  while  when  attached  to  d, 
it  divides  into  eight  ventral  segments.  The  number  of 
the  ventral  segments  is  proportional  to  the  rapidity  of 
vibration.  It  is  evident  that  we  have  here,  in  a  more 
delicate  form,  a  result  which  we  have  already  established 
in  the  case  of  our  India-rubber  tube  set  in  motion  by  the 
hand.  It  is  also  plain  that  this  result  might  be  deduced 
theoretically  from  our  first  law. 

We  may  extend  the  experiment.  Here  are  two  tuning- 
forks  separated  from  each  other  by  the  musical  interval 
called  a  fifth.  Attaching  a  string  to  one  of  the  forks,  I 
stretch  the  string  until  it  divides  into  two  ventral  seg- 
ments: attached  to  the  other  fork,  and  stretched  by  the 
same  weight,  it  divides  instantly  into  three  segments  when 
the  fork  is  set  in  vibration.  Now,  to  form  the  interval  of 
a  fifth,  the  vibrations  of  the  one  fork  must  be  to  those 
of  the  other  in  the  ratio  of  2:3.  The  division  of  the 
string,  therefore,  declares  the  interval.  In  the  same  way 
the  division  of  the  string  in  relation  to  all  other  musical 
intervals  may  be  illustrated.1 

Again.  Here  are  two  tuning-forks,  a  and  &,  one  of 
which  (a)  vibrates  twice  as  rapidly  as  the  other.  A  string 
of  silk  is  attached  to  a,  and  stretched  until  it  synchronizes 
with  the  fork,  and  vibrates  as  a  whole.  Here  is  a  second 
string  of  the  same  length,  formed  by  laying  four  strands 
of  the  first  one  side  by  side.  I  attach  this  compound 
thread  to  b,  and,  keeping  the  tension  the  same  as  in  the 
last  experiment,  set  b  in  vibration.  The  compound  thread 

1  The  subject  of  musical  intervals  will  be  treated  in  a  subsequent 
lecture. 


LAWS  OF   VIBRATION.  141 

synchronizes  with  6,  and  swings  as  a  whole.  Hence,  as 
the  fork  &  vibrates  with  half  the  rapidity  of  a,  by  quad- 
rupling the  weight  of  the  string  we  halved  its  rapidity  of 
vibration.  In  the  same  simple  way  it  might  be  proved 
that  by  augmenting  the  weight  of  the  string  nine  times 
we  reduce  the  number  of  its  vibrations  to  one-third.  We 
thus  demonstrate  the  law: 

The  rapidity  of  vibration  is  inversely  proportional  to 
the  square  root  of  the  weight  of  the  string. 

An  instructive  confirmation  of  this  result  is  thus  ob- 
tained: Attached  to  this  tuning-fork  is  a  silk  string  six 
feet  long.  Two  feet  of  the  string  are  composed  of  four 
strands  of  the  single  thread,  placed  side  by  side;  the  re- 
maining four  feet  are  a  single  thread.  A  stretching  force 
is  applied,  which  causes  the  string  to  divide  into  two  ven- 
tral segments.  But  how  does  it  divide?  Not  at  its  centre, 
as  is  the  case  when  the  string  is  of  uniform  thickness 
throughout,  but  at  the  precise  point  where  the  thick  string- 
terminates.  This  thick  segment,  two  feet  long,  is  now 
vibrating  at  the  same  rate  as  the  thin  segment  four  feet 
long,  a  result  which  follows  by  direct  deduction  from  the 
two  laws  already  established. 

Here  again  are  two  strings  of  the  same  length  and 
thickness.  One  of  them  is  attached  to  the  fork  a,  the 
other  to  the  fork  &,  which  vibrates  with  twice  the  rapidity 
of  a.  Stretched  by  a  weight  of  20  grains,  the  string 
attached  to  6  vibrates  as  a  whole.  Substituting  &  for  a,  a 
weight  of  80  grains  causes  the  string  to  vibrate  as  a 
whole.  Hence,  to  double  the  rapidity  of  vibration,  we 
must  quadruple  the  stretching  weight.  In  the  same  way 
it  might  be  proved  that  to  treble  the  rapidity  of  vibra- 
tion we  should  have  to  make  the  stretching  weight  nine- 
fold. Hence  our  third  law : 

The  rapidity  of  vibration  is  proportional  to  the  square 
root  of  the  tension. 


142 


SOUND. 


Let  us  vary  this  experiment.  This  silk  cord  is  carried 
from  the  tuning-fork  over  the  pulley,  and  stretched  by  a 
weight  of  80  grains.  The  string  vibrates  as  a  whole  as 
at  A,  Fig.  50.  By  diminishing  the  weight  the  string  is 


relaxed,  and  finally  divides  sharply  into  two  ventral  seg- 
ments, as  at  B,  Fig.  50.  What  is  now  the  stretching 
weight? — 20  grains,  or  one-fourth  of  the  first.  With  a 
stretching  weight  of  almost  exactly  9  grains  it  divides  into 
three  segments,  as  at  c;  while  with  a  stretching  weight 
of  5  grains  it  divides  into  four  segments,  as  at  D.  Thus, 


TIMBRE:  KLANGFARBE:  CLANG-TINT.  143 

I 

then,  a  tension  of  one-fourth  doubles,  a  tension  of  one- 
ninth  trebles,  and  a  tension  of  one-sixteenth  quadruples 
the  number  of  ventral  segments.  In  general  terms,  the 
number  of  segments  is  inversely  proportional  to  the  square 
root  of  the  tension.  This  result  may  be  deduced  by  rea- 
soning from  our  first  and  third  laws,  and  its  realization 
here  confirms  their  correctness. 

Thus,  by  a  series  of  reasonings  and  experiments  totally 
different  from  those  formerly  employed,  we  arrive  at 
the  self-same  laws.  In  science,  different  lines  of  reason- 
ing often  converge  upon  the  same  truth;  and  if  we  only 
follow  them  faithfully,  we  are  sure  to  reach  that  truth  at 
last.  We  may  emerge,  and  often  do  emerge,  from  our 
reasoning  with  a  contradiction  in  our  hands;  but  on  re- 
tracing our  steps,  we  infallibly  find  the  cause  of  the  con- 
tradiction to  be  due,  not  to  any  lack  of  constancy  in  Na- 
ture, but  of  accuracy  in  man.  It  is  the  millions  of  ex- 
periences of  this  kind  which  science  furnishes  that  give 
us  our  present  faith  in  the  stability  of  Nature. 


HARMONIC  SOUNDS  OR  OVERTONES. 

§  9.  Timbre;  Klangfarbe;  Clang-tint. 

We  now  approach  a  portion  of  our  subject  which  will 
subsequently  prove  to  be  of  the  very  highest  importance. 
It  has  been  shown  by  the  most  varied  experiments  that 
a  stretched  string  can  either  vibrate  as  a  whole,  or  di- 
vide itself  into  a  number  of  equal  parts,  each  of  which 
vibrates  as  an  independent  string.  Now  it  is  not  possible 
to  sound  the  string  as  a  whole  without  at  the  same  time 
causing,  to  a  greater  or  less  extent,  its  subdivision;  that 
is  to  say,  superposed  upon  the  vibrations  of  the  whole 
string  we  have  always,  in  a  greater  or  less  degree,  the 

vibrations  of  its  aliquot  parts.    The  higher  notes  produced 
10 


144  SOUND. 

by  these  latter  vibrations  are  called  the  harmonics  of  the 
string.  And  so  it  is  with  other  sounding  bodies;  we  have 
in  all  cases  a  coexistence  of  vibrations.  Higher  tones 
mingle  with  the  fundamental  one,  and  it  is  their  inter- 
mixture which  determines  what,  for  want  of  a  better 
term,  we  call  the  quality  of  the  sound.  The  French  call 
it  timbre,  and  the  Germans  call  it  Klangfarbe.1  It  is  this 
union  of  high  and  low  tones  that  enables  us  to  distinguish 
one  musical  instrument  from  another.  A  clarionet  and  a 
violin,  for  example,  though  tuned  to  the  same  fundamental 
note,  are  not  confounded;  the  auxiliary  tones  of  the  one 
are  different  from  those  of  the  other,  and  these  latter 
tones,  uniting  themselves  to  the  fundamental  tones  of  the 
two  instruments,  destroy  the  identity  of  the  sounds. 

All  bodies  and  instruments,  then,  employed  for  pro- 
ducing musical  sounds  emit,  besides  their  fundamental 
tones,  others  due  to  higher  orders  of  vibration.  The  Ger- 
mans embrace  all  such  sounds  under  the  general  term 
Obertone.  I  think  it  will  be  an  advantage  if  we  in  Eng- 
land adopt  the  term  overtones  as  the  equivalent  of  the 
term  employed  in  Germany.  One  has  occasion  to  envy 
the  power  of  the  German  language  to  adapt  itself  to 
requirements  of  this  nature.  The  term  Klangfarbe,  for 
example,  employed  by  Helmholtz  is  exceedingly  expres- 
sive, and  we  need  its  equivalent  also.  Color  depends  upon 
rapidity  of  vibration,  blue  light  bearing  to  red  the  same 
relation  that  a  high  tone  does  to  a  low  one.  A  simple 
color  has  but  one  rate  of  vibration,  and  it  may  be  regarded 
as  the  analogue  of  a  simple  tone  in  music.  A  tone,  then, 
may  be  defined  as  the  product  of  a  vibration  which  cannot 
be  decomposed  into  more  simple  ones.  A  compound 
color,  on  the  contrary,  is  produced  by  the  admixture  of 
two  or  more  simple  ones,  and  an  assemblage  of  tones,  such 

1  "  This  quality  of  sound,  sometimes  called  its  register,  color,  or 
timbre." — (Thomas  Young,  "  Essay  on  Music.") 


RELATION  OF  POINT  PLUCKED  TO  OVERTONES.  145 

as  we  obtain  when  the  fundamental  tone  and  the  har- 
monics of  a  string  sound  together,  is  called  by  the  Germans 
a  Klang.  May  we  not  employ  the  English  word  clang 
to  denote  the  same  thing,  and  thus  give  the  term  a  pre- 
cise scientific  meaning  akin  to  its  popular  one?  And  may 
we  not,  like  Helmholtz,  add  the  word  color  or  tint,  to 
denote  the  character  of  the  clang,  using  the  term  clang- 
tint  as  the  equivalent  of  Klangfarbe? 

With  your  permission  I  shall  henceforth  employ  these 
terms;  and  now  it  becomes  our  duty  to  look  a  little 
more  closely  than  we  have  hitherto  done  into  the  sub- 
division of  a  string  into  its  harmonic .  segments.  Our 
monochord  with  its  stretched  wire  is  before  you.  The 
scale  of  the  instrument  is  divided  into  100  equal  parts. 
At  the  middle  point  of  the  wire  stands  the  number  50;  at 
a  point  almost  exactly  one-third  of  its  length  from  its 
end  stands  the  number  33;  while  at  distances  equal  to 
one-fourth  and  one-fifth  of  its  length  from  its  end  stand 
the  numbers  25  and  20  respectively.  These  numbers 
are  sufficient  for  our  present  purpose.  When  the  wire 
is  plucked  at  50  you  hear  its  clang,  rather  hollow  and 
dull.  When  plucked  at  33,  the  clang  is  different.  When 
plucked  at  25,  the  clang  is  different  from  either  of  the 
former.  As  we  retreat  from  the  centre  of  the  string,  the 
clang-tint  becomes  more  "  brilliant,"  the  sound  more  brisk 
and  sharp.  What  is  the  reason  of  these  differences  in  the 
sound  of  the  same  wire? 

The  celebrated  Thomas  Young,  once  professor  in  this 
Institution,  enables  us  to  solve  the  question.  He  proved 
that  when  any  point  of  a  string  is  plucked,  all  the  higher 
tones  which  require  that  point  for  a  node  vanish  from  the 
clang.  Let  me  illustrate  this  experimentally.  I  pluck 
the  point  50,  and  permit  the  string  to  sound.  It  may  be 
proved  that  the  first  overtone,  which  corresponds  to  a  di- 
vision of  the  string  into  two  vibrating  parts,  is  now  absent 


146  SOUND. 

from  the  clang.  If  it  were  present,  the  damping  of  the 
point  50  would  not  interfere  with  it,  for  this  point  would 
be  its  node.  But  on  damping  the  point  50  the  fundamen- 
tal tone  is  quenched,  and  no  octave  of  that  tone  is  heard. 
Along  with  the  octave  its  whole  progeny  of  overtones, 
with  rates  of  vibration  four  times,  six  times,  eight  times — 
all  even  numbers  of  times — the  rate  of  the  fundamental 
tone,  disappear  from  the  clang.  All  these  tones  require 
that  a  node  should  exist  at  the  centre,  where,  according 
to  the  principle  of  Young,  it  cannot  now  be  formed. 
Let  us  pluck  some  other  point,  say  25,  and  damp  50  as 
before.  The  fundamental  tone  is  now  gone,  but  its  oc- 
tave, clear  and  full,  rings  in  your  ears.  The  point  50  in 
this  case  not  being  the  one  plucked,  a  node  can  form 
there;  it  has  formed,  and  the  two  halves  of  the  string 
continue  to  vibrate  after  the  vibrations  of  the  string  as  a 
whole  have  been  extinguished.  Plucking  the  point  33, 
the  second  harmonic  or  overtone  is  absent  from  the  clang. 
This  is  proved  by  damping  the  point  33.  If  the  second 
harmonic  were  on  the  string  this  would  not  affect  it,  for 
33  is  its  node.  The  fundamental  is  quenched,  but  no  tone 
corresponding  to  a  division  of  the  string  into  three  vibrat- 
ing parts  is  now  heard.  The  tone  is  not  heard  because  it 
was  never  there. 

All  the  overtones  which  depend  on  this  division,  those 
with  six  times,  nine  times,  twelve  times  the  rate  of  vibra- 
tion of  the  fundamental  one,  are  also  withdrawn  from 
the  clang.  Let  us  now  pluck  20,  damping  33  as  before. 
The  second  harmonic  is  not  extinguished,  but  continues 
to  sound  clearly  and  fully  after  the  extinction  of  the  fun- 
damental tone.  In  this  case  the  point  33  not  being  that 
plucked,  a  node  can  form  there,  and  the  string  can  divide 
itself  into  three  parts  accordingly.  In  like  manner,  if  25 
be  plucked  and  then  damped,  the  third  harmonic  is  not 
heard;  but  when  a  point  between  25  and  the  end  of  the 


MINGLING  OF  OVERTONES  WITH  FUNDAMENTAL.  147 

wire  is  plucked,  and  the  point  25  damped,  the  third  har- 
monic is  plainly  heard.  And  thus  we  might  proceed,  the 
general  rule  enunciated  by  Young,  and  illustrated  by 
these  experiments,  being,  that  when  any  point  of  a  string 
is  plucked  or  struck,  or,  as  Helmholtz  adds,  agitated  with 
a  bow,  the  harmonic  which  requires  that  point  for  a  node 
vanishes  from  the  general  clang  of  the  string. 

§  10.  Mingling  of  Overtones  with  fundamental. 
The  ^Eolian  Harp. 

You  are  now  in  a  condition  to  estimate  the  influence 
which  these  higher  vibrations  must  have  upon  the  quality 
of  the  tone  emitted  by  the  string.  The  sounds  which  ring 
in  your  ears  so  plainly  after  the  fundamental  tone  is 
quenched  mingled  with  that  note  before  it  was  extin- 
guished. It  seems  strange  that  tones  of  such  power  could 
be  so  masked  by  the  fundamental  one  that  even  the  disci- 
plined ear  of  a  musician  is  unable  to  separate  the  one  from 
the  other.  But  Helmholtz  has  shown  that  this  is  due  to 
want  of  practice  and  attention.  The  musician's  faculties 
were  never  exercised  in  this  direction.  There  are  numer- 
ous effects  which  the  musician  can  distinguish,  because 
his  art  demands  the  habit  of  distinguishing  them.  But  it 
is  no  necessity  of  his  art  to  resolve  the  clang  of  an  instru- 
ment into  its  constituent  tones.  By  attention,  however, 
even  the  unaided  ear  can  accomplish  this,  particularly  if 
the  mind  be  informed  beforehand  what  the  ear  has  to  bend 
itself  to  find. 

And  this  reminds  me  of  an  occurrence  which  took 
place  in  this  room  at  the  beginning  of  my  acquaintance 
with  Faraday.  I  wished  to  show  him  a  peculiar  action  of 
an  electro-magnet  upon  a  crystal.  Everything  was  ar- 
ranged, when  just  before  the  magnet  was  excited  he  laid 
his  hand  upon  my  arm  and  asked,  "  What  am  I  to  look 
for? "  Amid  the  assemblage  of  impressions  connected 


148  SOUND. 

with  an  experiment,  even  this  prince  of  experimenters  felt 
the  advantage  of  having  his  attention  directed  to  the  spe- 
cial point  to  be  illustrated.  Such  help  is  the  more  needed 
when  we  attempt  to  resolve  into  its  constituent  parts  an 
effect  so  intimately  blended  as  the  composite  tones  of  a 
clang.  When  we  desire  to  isolate  a  particular  tone,  one 
way  of  helping  the  attention  is  to  sound  that  tone  feebly 
on  a  string  of  the  proper  length.  Thus  prepared,  the  ear 
glides  more  readily  from  the  single  tone  to  that  of  the 
same  pitch  in  a  composite  clang,  and  detaches  it  more 
readily  from  its  companions.  In  the  experiments  executed 
a  moment  ago,  where  our  aim  in  each  respective  case  was 
to  bring  out  the  higher  tone  of  the  string  in  all  its  power, 
we  entirely  extinguished  its  fundamental  tone.  It  may, 
however,  be  enfeebled  without  being  destroyed.  I  pluck 
this  string  at  33,  and  lay  the  feather  lightly  for  a  moment 
on  the  string  at  50.  The  fundamental  tone  is  thereby  so 
much  lowered  that  its  octave  can  make  itself  plainly  heard.' 
By  again  touching  the  string  at  50,  the  fundamental  tone 
is  lowered  still  more;  so  that  now  its  first  harmonic  is 
more  powerful  than  itself.  You  hear  the  sound  of  both, 
and  you  might  have  heard  them  in  the  first  instance  by  a 
sufficient  stretch  of  attention. 

The  harmonics  of  a  string  may  be  augmented  or  sub^ 
dued  within  wide  limits.  They  may,  as  we  have  seen,  be 
masked  by  the  fundamental  tone,  and  they  may  also  effect- 
ually mask  it.  A  stroke  with  a  hard  body  is  favorable, 
while  a  stroke  with  a  soft  body  is  unfavorable  to  their 
development.  They  depend,  moreover,  on  the  promptness 
with  which  the  body  striking  the  string  retreats  after 
striking.  Thus  they  are  influenced  by  the  weight  and 
elasticity  of  the  hammers  in  the  pianoforte.  They  also  de- 
pend upon  the  place  at  which  the  shock  is  imparted.  "When, 
for  example,  a  string  is  struck  in  the  centre,  the  harmonics 
are  less  powerful  than  when  it  is  struck  near  one  end. 


THE  CLANG  OP  PIANO-WIRES.  149 

Helmholtz,  who  is  equally  eminent  as  a  mathematician 
and  as  an  experimental  philosopher,  has  calculated  the 
theoretic  intensity  of  the  harmonics  developed  in  various 
ways;  that  is  to  say,  the  actual  vis  viva  or  energy  of  the 
vibration,  irrespective  of  its  effects  upon  the  ear.  A  single 
example  given  by  him  will  suffice  to  illustrate  this  subject. 
Calling  the  intensity  of  the  fundamental  tone,  in  each 
case,  100,  that  of  the  second  harmonic,  when  the  string 
was  simply  pulled  aside  at  a  point  |th  of  its  length  from 
its  end  and  then  liberated,  was  found  to  be  56.1,  or  a  little 
better  than  one-half.  When  the  string  was  struck  with 
the  hammer  of  a  pianoforte,  whose  contact  with  the  string 
endured  for  f  ths  of  the  period  of  vibration  of  the  funda- 
mental tone,  the  intensity  of  the  same  tone  was  9.  In  this 
case  the  second  harmonic  was  nearly  quenched.  When, 
however,  the  duration  of  contact  was  diminished  to  /Tj-ths 
of  the  period  of  the  fundamental,  the  intensity  of  the  har- 
monic rose  to  357;  while,  when  the  string  was  sharply 
struck  with  a  very  hard  hammer,  the  intensity  mounted  to 
505,  or  to  more  than  quintuple  that  of  the  fundamental 
tone.1  Pianoforte  manufacturers  have  found  that  the 
most  pleasing  tone  is  excited  by  the  middle  strings  of  their 
instruments,  when  the  point  against  which  the  hammer 
strikes  is  from  -if-th  to  -j-th  of  the  length  of  the  wire  from 
its  extremity. 

Why  should  this  be  the  case?  Helmholtz  has  given 
the  answer.  Up  to  the  tones  which  require  these  points 
as  nodes  the  overtones  all  form  cords  with  the  funda- 
mental ;  but  the  sixth  and  eighth  overtones  of  the  wire  do 
not  enter  into  such  chords;  they  are  dissonant  tones,  and 
hence  the  desirability  of  doing  away  with  them.  This  is 
accomplished  by  making  the  point  at  which  a  node  is  re- 
quired that  on  which  the  hammer  falls.  The  possibility 
of  the  tone  forming  is  thereby  shut  out,  and  its  injurious 
effect  is  avoided. 

1  "  Lehre  von  den  Tonempfindungen,"  p.  135. 


150  SOUND. 

The  strings  of  the  ^olian  harp  are  divided  into  har- 
monic parts  by  a  current  of  air  passing  over  them.  The 
instrument  is  usually  placed  in  a  window  between  the  sash 
and  frame,  so  as  to  leave  no  way  open  to  the  entrance  of 
the  air  except  over  the  strings.  Sir  Charles  Wheatstone 
recommends  the  stretching  of  a  first  violin-string  at  the 
bottom  of  a  door  which  does  not  closely  fit.  When  the 
door  is  shut,  the  current  of  air  entering  beneath  sets  the 
string  in  vibration,  and  when  a  fire  is  in  the  room,  the  vi- 
brations are  so  intense  that  a  great  variety  of  sounds  are 
simultaneously  produced.1  A  gentleman  in  Basle  once 
constructed  with  iron  wires  a  large  instrument  which  he 
called  the  weather-harp  or  giant-harp,  and  which,  accord- 
ing to  its  maker,  sounded  as  the  weather  changed.  Its 
sounds  were  also  said  to  be  evoked  by  changes  of  terres- 
trial magnetism.  Chladni  pointed  out  the  error  of  these 
notions,  and  reduced  the  action  of  the  instrument  to  that 
of  the  wind  upoa  its  strings. 

§  11.  Young's  Optical  Illustrations. 

Finally,  with  regard  to  the  vibrations  of  a  wire,  the 
experiments  of  Dr.  Young,  who  was  the  first  to  employ 
optical  methods  in  such  experiments,  must  be  mentioned. 
He  allowed  a  sheet  of  sunlight  to  cross  a  pianoforte-wire, 
and  obtained  thus  a  brilliant  dot.  Striking  the  wire  he 
caused  it  to  vibrate,  the  dot  described  a  luminous  line  like 
that  produced  by  the  whirling  of  a  burning  coal  in  the  air, 
and  the  form  of  this  line  revealed  the  character  of  the  vi- 
bration. It  was  rendered  manifest  by  these  experiments 
that  the  oscillations  of  the  wire  were  not  confined  to  a 
single  plane,  but  that  it  described  in  its  vibrations  curves 
of  greater  or  less  complexity.  Superposed  upon  the  vi- 

1  The  action  of  such  a  string  is  substantially  the  same  as  that  of  the 
siren.  The  string  renders  intermittent  the  current  of  air.  Its  action 
also  resembles  that  of  a  reed.  See  Lecture  V. 


YOUNG'S  OPTICAL  ILLUSTRATIONS. 


151 


bration  of  the  whole  string  were  partial  vibrations,  which 
revealed  themselves  as  loops  and  sinuosities.  Some  of  the 
lines  observed  by  Dr.  Young  are  given  in  Fig.  51.  Every 


FIG.  51. 


one  of  these  figures  corresponds  to  a  distinct  impression 
made  by  the  wire  upon  the  surrounding  air.  The  form  of 
the  sonorous  wave  is  affected  by  these  superposed  vibra- 
tions, and  thus  they  influence  the  clang-tint  or  quality  of 
the  sound. 


152  SOUND. 


SUMMARY  OF  CHAPTER  III. 

THE  amount  of  motion  communicated  by  a  vibrating 
string  to  the  air  is  too  small  to  be  perceived  as  sound, 
even  at  a  small  distance  from  the  string. 

When  a  broad  surface  vibrates  in  air,  condensations 
and  rarefactions  are  more  readily  formed  than  when  the 
vibrating  body  is  of  small  dimensions  like  a  string. 
Hence,  when  strings  are  employed  as  sources  of  musical 
sounds,  they  are  associated  with  surfaces  of  larger  area 
which  take  up  their  vibrations,  and  transfer  them  to  the 
surrounding  air. 

Thus  the  tone  of  a  harp,  a  piano,  a  guitar,  or  a  violin, 
depends  mainly  upon  the  sound-board  of  the  instrument. 

The  following  four  laws  regulate  the  vibrations  of 
strings:  The  rate  of  vibrations  is  inversely  proportional  to 
the  length;  it  is  inversely  proportional  to  the  diameter;  it 
is  directly  proportional  to  the  square  root  of  the  stretching 
weight  or  tension;  and  it  is  inversely  proportional  to  the 
square  root  of  the  density  of  the  string. 

When  strings  of  different  diameters  and  densities  are 
compared,  the  law  is,  that  the  rate  of  vibration  is  in- 
versely proportional  to  the  square  root  of  the  weight  of 
the  string. 

When  a  stretched  rope,. or  an  India-rubber  tube  filled 
with  sand,  with  one  of  its  ends  attached  to  a  fixed  object, 
receives  a  jerk  at  the  other  end,  the  protuberance  raised 
upon  the  tube  runs  along  it  as  a  pulse  to  the  fixed  end, 
and,  being  there  reflected,  returns  to  the  hand  by  which 
the  jerk  was  imparted. 


SUMMAKY.  153 

The  time  required  for  the  pulse  to  travel  from  the 
hand  to  the  fixed  end  of  the  tube  and  back  is  that  re- 
quired by  the  whole  tube  to  execute  a  complete  vibration. 

When  a  series  of  pulses  are  sent  in  succession  along 
the  tube,  the  direct  and  reflected  pulses  meet,  and  by  their 
coalescence  divide  the  tube  into  a  series  of  vibrating  parts, 
called  ventral  segments,  which  are  separated  from  each 
other  by  points  of  apparent  rest  called  nodes. 

The  number  of  ventral  segments  is  directly  propor- 
tional to  the  rate  of  vibration  at  the  free  end  of  the  tube. 

The  hand  which  produces  these  vibrations  may  move 
through  less  than  an  inch  of  space;  while  by  the  accumu- 
lation of  its  impulses  the  amplitude  of  the  ventral  seg- 
ments may  amount  to  several  inches,  or  even  to  several 
feet. 

If  an  India-rubber  tube,  fixed  at  both  ends,  be  encir- 
cled at  its  centre  by  the  finger  and  thumb,  when  either  of 
its  halves  is  pulled  aside  and  liberated,  both  halves  are 
thrown  into  a  state  of  vibration. 

If  the  tube  be  encircled  at  a  point  one-third,  one- 
fourth,  or  one-fifth  of  its  length  from  one  of  its  ends,  on 
pulling  the  shorter  segment  aside  and  liberating  it,  the 
longer  segment  divides  itself  into  two,  three,  or  four 
vibrating  parts,  separated  from  each  other  by  nodes. 

The  number  of  vibrating  segments  depends  upon  the 
rate  of  vibration  at  the  point  encircled  by  the  finger  and 
thumb. 

Here  also  the  amplitude  of  vibration  at  the  place  en- 
circled by  the  finger  and  thumb  may  not  be  more  than  a 
fraction  of  an  inch,  while  the  amplitude  of  the  ventral 
segments  may  amount  to  several  inches. 

A  musical  string  damped  by  a  feather  at  a  point  one- 
half,  one-third,  one-fourth,  one-fifth,  etc.,  of  its  length 
from  one  of  its  ends,  and  having  its  shorter  segment  agi- 
tated, divides  itself  exactly  like  the  India-rubber  tube. 


154:  SOUND. 

Its  division  may  be  rendered  apparent  by  placing  little 
paper  riders  across  it.  Those  placed  at  the  ventral  seg- 
ments are  thrown  off,  while  those  placed  at  the  nodes 
retain  their  places. 

The  notes  corresponding  to  the  division  of  a  string 
into  its  aliquot  parts  are  called  the  harmonics  of  the 
string. 

When  a  string  vibrates  as  a  whole,  it  usually  divides  at 
the  same  time  into  its  aliquot  parts.  Smaller  vibrations 
are  superposed  upon  the  larger,  the  tones  corresponding  to 
those  smaller  vibrations,  and  which  we  have  agreed  to  call 
overtones,  mingling  at  the  same  time  with  the  funda- 
mental tone  of  the  string. 

The  addition  of  these  overtones  to  the  fundamental 
tone  determines  the  timbre  or  quality  of  the  sound,  or,  as 
we  have  agreed  to  call  it,  the  clang-tint. 

It  is  the  addition  of  such  overtones  to  fundamental 
tones  of  the  same  pitch  which  enables  us  to  distinguish 
the  sound  of  a  clarionet  from  that  of  a  flute,  and  the 
sound  of  a  violin  from  both.  Could  the  pure  fundamental 
tones  of  these  instruments  be  detached,  they  would  be 
undistinguishable  from  each  other;  but  the  different  ad- 
mixture of  overtones  in  the  different  instruments  renders 
their  clang-tints  diverse,  and  therefore  distinguishable. 

Instead  of  the  heavy  India-rubber  tube  in  the  experi- 
ment above  referred  to,  we  may  employ  light  silk  strings, 
and,  instead  of  the  vibrating  hand,  we  may  employ  vibrat- 
ing tuning-forks,  and  cause  the  strings  to  swing  as  a  whole, 
or  to  divide  themselves  into  any  number  of  ventral  seg- 
ments. Effects  of  great  beauty  are  thus  obtained,  and  by 
experiments  of  this  character  all  the  laws  of  vibrating 
strings  may  be  demonstrated. 

When  a  stretched  string  is  plucked  aside  or  agitated 
by  a  bow,  all  the  overtones  which  require  the  agitated 
point  for  a  node  vanish  from  the  clang  of  the  string. 


SUMMARY.  155 

The  point  struck  by  the  hammer  of  the  piano  is  from 
one-seventh  to  one-ninth  of  the  length  of  the  string  from 
its  end:  by  striking  this  point,  the  notes  which  require  it 
as  a  node  cannot  be  produced,  a  source  of  dissonance  being 
thus  avoided. 


CHAPTEK  IV. 

Vibrations  of  a  Rod  fixed  at  Both  Ends :  its  Subdivisions  and  Corre- 
sponding Overtones. — Vibrations  of  a  Rod  fixed  at  One  End. — The 
Kaleidophone.— The  Iron  Fiddle  and  Musical  Box.— Vibrations  of 
a  Rod  free  at  Both  Ends.— The  Claque-bois  and  Glass  Harmonica. 
— Vibrations  of  a  Tuning- Fork :  its  Subdivision  and  Overtones. — 
Vibrations  of  Square  Plates.— Chladni's  Discoveries.— Wheatstone's 
Analysis  of  the  Vibrations  of  Plates. — Chladni's  Figures. — Vibra- 
tions of  Disks  and  Bells. — Experiments  of  Faraday  and  Strehlke. 

§  1.  Transverse  Vibrations  of  a  Rod  fixed  at  Both  Ends. 

OUR  last  chapter  was  devoted  to  the  transverse  vibra- 
tions of  strings.  This  one  I  propose  devoting  to  the  trans- 
verse vibrations  of  rods,  plates,  and  bells,  commencing 
with  the  case  of  a  rod  fixed  at  both  ends.  Its  modes  of 
vibration  are  exactly  those  of  a  string.  It  vibrates  as  a 
whole,  and  can  also  divide  itself  into  two,  three,  four,  or 
more  vibrating  parts.  But,  for  a  reason  to  be  immediately 
assigned,  the  laws  which  regulate  the  pitch  of  the  succes- 
sive notes  are  entirely  different  in  the  two  cases.  Thus, 
when  a  string  divides  into  two  equal  parts,  each  of  its 
halves  vibrates  with  twice  the  rapidity  of  the  whole; 
while,  in  the  case  of  the  rod,  each  of  its  halves  vibrates 
with  nearly  three  times  the  rapidity  of  the  whole.  With 
greater  strictness,  the  ratio  of  the  two  rates  of  vibration  is 
as  9  is  to  25,  or  as  the  square  of  3  to  the  square  of  5.  In 
Fig.  52,  a  a',  c  c',  &  &',  d  d',  are  sketched  the  first  four 
modes  of  vibration  of  a  rod  fixed  at  both  ends :  the  succes- 
sive rates  of  vibration  in  the  four  cases  bear  to  each  other 
the  following  relation: 

Number  of  nodes  .    0  1  2  3 

Number  of  vibrations    .9  25  49  81 

156 


TRANSVERSE  VIBRATIONS  OF  RODS  FIXED  AT  END.  157 

the  last  row  of  figures  being  the  squares  of  the  odd  num- 
bers 3,  5,  7,  9. 

In  the  case  of  a  string,  the  vibrations  are  maintained 
by  a  tension  externally  applied;  in  the  case  of  a  rod,  the 
vibrations  are  maintained  by  the  elasticity  of  the  rod 
itself.  The  modes  of  division  are  in  both  cases  the  same, 

FIG.  52. 


I 


but  the  forces  brought  into  play  are  different,  and  hence 
also  the  successive  rates  of  vibration. 

§  2.  Transverse  Vibrations  of  a  Rod  fixed  at  One  End. 

Let  us  now  pass  on  to  the  case  of  a  rod  fixed  at  one  end 
and  free  at  the  other.  Here  also  it  is  the  elasticity  of  the 
material,  and  not  any  external  tension,  that  sustains  the 
vibrations.  Approaching,  as  usual,  sonorous  vibrations 
through  more  grossly  mechanical  ones,  I  fix  this  long  rod 
of  iron,  n  o,  Fig.  53,  in  a  vice,  draw  it  aside,  and  liberate 
it.  To  make  its  vibrations  more  evident,  its  shadow  is 
thrown  upon  a  screen.  The  rod  oscillates  as  a  whole  to 
and  fro,  between  the  points  p  p'.  But  it  is  capable  of 
other  modes  of  vibration.  Damping  it  at  the  point  a,  by 
holding  it  gently  there  between  the  finger  and  thumb, 
and  striking  it  sharply  between  a  and  o,  the  rod  divides 
into  two  vibrating  parts,  separated  by  a  node  as  shown  in 
Fig.  54.  You  see  upon  the  screen  a  shadowy  spindle  be- 
tween a  and  the  vice  below,  and  a  shadowy  fan  above  a, 
with  a  black  node  between  both.  The  division  may  be 
effected  without  damping  a,  by  merely  imparting  a  suffi- 
ciently sharp  shock  to  the  rod  between  a  and  o.  In  this 
case,  however,  besides  oscillating  in  parts,  the  rod  oscil- 


158 


SOUND. 


lates  as  a  whole,  the  partial  oscillations  being  superposed 
upon  the  large  one. 

You  notice,  moreover,  that  the  amplitude  of  the  par- 
tial oscillations  depends  upon  the  promptness  of  the  stroke. 
When  the  stroke  is  sluggish,  the  partial  division  is  but 
feebly  pronounced,  the  whole  oscillation  being  most 
marked.  But  when  the  shock  is  sharp  and  prompt,  the 
whole  oscillation  is  feeble,  and  the  partial  oscillations  are 


FIG.  54. 


FIG.  55. 


executed  with  vigor.  If  the  vibrations  of  this  rod  were 
rapid  enough  to  produce  a  musical  sound,  the  oscillation 
of  the  rod  as  a  whole  would  correspond  to  its  fundamental 
tone,  while  the  division  of  the  rod  into  two  vibrating  parts 
would  correspond  to  the  first  of  its  overtones.  If,  more- 
over, the  rod  vibrated  as  a  whole  and  as  a  divided  rod  at 
the  same  time,  the  fundamental  tone  and  the  overtone 


CHLADNI'S  TONOMETER.  159 

would  be  heard  simultaneously.  By  damping  the  proper 
point  and  imparting  the  proper  shock,  we  can  still  further 
subdivide  the  rod,  as  shown  in  Fig.  55. 

§  3.  Chladni's  Tonometer:  the  Iron  Fiddle,  Musical 
Box,  and  the  Kaleidophone. 

And  now  let  us  shorten  our  rod,  so  as  to  bring  its  vibra- 
tions into  proper  relation  to  our  ears.  When  it  is  about 
four  inches  long,  it  emits  a  low  musical  sound.  When 
further  shortened,  the  tone  is  higher;  and,  by  continuing 
to  shorten  the  rod,  the  speed  of  vibration  is  augmented, 
until  finally  the  sound  becomes  painfully  acute.  These 
musical  vibrations  differ  only  in  rapidity  from  the  grosser 
oscillations  which  a  moment  ago  appealed  to  the  eye. 

The  increase  in  the  rate  of  vibrations  here  observed  is 
ruled  by  a  definite  law;  the  number  of  vibrations  exe- 
cuted at  a  given  time  is  inversely  proportional  to  the 
square  of  the  length  of  the  vibrating  rod.  You  hear  the 
sound  of  this  strip  of  brass,  two  inches  long,  as  the  fiddle- 
bow  is  passed  over  its  end.  Making  the  length  of  the 
strip  one  inch,  the  sound  is  the  double  octave  of  the  last 
one;  the  rate  of  vibration  is  augmented  four  times.  Thus, 
by  doubling  the  length  of  the  vibrating  strip,  we  reduce 
its  rate  of  vibration  to  one-fourth ;  by  trebling  the  length, 
we  reduce  the  rate  of  vibration  to  one-ninth;  by  quad- 
rupling the  length,  we  reduce  the  vibrations  to  one- 
sixteenth,  and  so  on.  It  is  plain  that,  by  proceeding  in 
this  way,  we  should  finally  reach  a  length  where  the  vibra- 
tions would  be  sufficiently  slow  to  be  counted.  Or,  it  is 
plain  that,  beginning  with  a  long  strip  whose  vibrations 
could  be  counted,  we  might,  by  shortening,  not  only  make 
the  strip  sound,  but  also  determine  the  rates  of  vibration 
corresponding  to  its  different  tones.  Supposing  we  start 
with  a  strip  36  inches  long,  which  vibrates  once  in  a 
second,  the  strip  reduced  to  12  inches  would,  according  to 


160  SOUND. 

the  above  law,  execute  9  vibrations  a  second:  reduced  to 
6  inches,  it  would  execute  36,  to  3  inches,  144;  while,  if 
reduced  to  1  inch  in  length,  it  would  execute  1,296  vibra- 
tions in  a  second.  It  is  easy  to  fill  the  spaces  between  the 
lengths  here  given,  and  thus  to  determine  the  rate  of  vibra- 
tion corresponding  to  any  particular  tone.  This  method 
was  proposed  and  carried  out  by  Chladni. 

A  musical  instrument  may  be  formed  of  short  rods. 
Into  this  common  wooden  tray  a  number  of  pieces  of 
stout  iron  wire  of  different  lengths  are  fixed,  being  ranged 
in  a  semicircle.  When  the  fiddle-bow  is  passed  over  the 
series,  we  obtain  a  succession  of  very  pleasing  notes.  A 
competent  performer  could  certainly  extract  very  tolerable 
music  from  a  sufficient  number  of  these  iron  pins.  The 
iron  fiddle  (violon  de  fer)  is  thus  formed.  The  notes  of 
the  ordinary  musical  box  are  also  produced  by  the  vibra- 
tions of  tongues  of  metal  fixed  at  one  end.  Pins  are  fixed 
in  a  revolving  cylinder,  the  free  ends  of  the  tongues  are 
lifted  by  these  pins  and  then  suddenly  let  go.  The 
tongues  vibrate,  their  length  and  strength  being  so  ar- 
ranged as  to  produce  in  each  particular  case  the  proper 
rapidity  of  vibration. 

Sir  Charles  Wheatstone  has  devised  a  simple  and  in- 
genious optical  method  for  the  study  of  vibrating  rods 
fixed  at  one  end.  Attaching  light  glass  beads,  silvered 
within,  to  the  end  of  a  metal  rod,  and  allowing  the  light 
of  a  lamp  or  candle  to  fall  upon  the  bead,  he  obtained  a 
small  spot  intensely  illuminated.  When  the  rod  vibrated, 
this  spot  described  a  brilliant  line  which  showed  the  char- 
acter of  the  vibration.  A  knitting-needle,  fixed  in  a  vice 
with  a  small  bead  stuck  on  to  it  by  marine  glue,  answers 
perfectly  as  an  illustration.  In  Wheatstone's  more  com- 
plete instrument,  which  he  calls  a  kaleidophone,  the  vi- 
brating rods  are  firmly  screwed  into  a  massive  stand.  Ex- 
tremely beautiful  figures  are  obtained  by  this  simple  con- 


THE  KALEIDOPHONE.  161 

trivance,  some  of  which  may  now  be  projected  on  a 
magnified  scale  upon  the  screen  before  you. 

Fixing  the  rod  horizontally  in  the  vice,  a  condensed 
beam  is  permitted  to  fall  upon  the  silvered  bead,  a  spot  of 
sunlike  brilliancy  being  thus  obtained.  Placing  a  lens  in 
front  of  the  bead,  a  bright  image  of  the  spot  is  thrown 
upon  the  screen,  the  needle  is  then  drawn  aside,  and 
suddenly  liberated.  The  spot  describes  a  ribbon  of  light, 
at  first  straight,  but  speedily  opening  out  into  an  ellipse, 
passing  into  a  circle,  and  then  again  through  a  second 
ellipse  back  to  a  straight  line.  This  is  due  to  the  fact  that 
a  rod  held  thus  in  a  vice  vibrates  not  only  in  the  direction 
in  which  it  is  drawn  aside,  but  also  at  right  angles  to  this 
direction.  The  curve  is  due  to  the  combination  of  two 
rectangular  vibrations.1  While  the  rod  is  thus  swinging  as 
a  whole,  it  may  also  divide  itself  into  vibrating  parts.  By 
properly  drawing  a  violin-bow  across  the  needle,  this  ser- 
rated circle,  Fig.  56,  is  obtained,  a  number  of  small  undu- 
lations being  superposed  upon  the  large 
one.  You  moreover  hear  a  musical 
tone,  which  you  did  not  hear  when  the 
rod  vibrated  as  a  whole  only;  its  oscil- 
lations, in  fact,  were  then  too  slow 
to  excite  such  a  tone.  The  vibrations 
which  produce  these  sinuosities,  and 
which  correspond  to  the  first  division 
of  the  rod,  are  executed  with  about  6|  times  the  rapid- 
ity of  the  vibrations  of  the  rod  swinging  as  a  whole. 
Again  I  draw  the  bow;  the  note  rises  in  pitch,  the  ser- 
rations run  more  closely  together,  forming  on  the  screen 
a  luminous  ripple  more  minute  and,  if  possible,  more 

1  Chladni  also  observed  this  compounding  of  vibrations,  and  exe- 
cuted a  series  of  experiments,  which,  in  their  developed  form,  are  those 
of  the  kaleidophone.  The  composition  of  vibrations  will  be  studied  at 
some  length  in  a  subsequent  lecture. 


162 


SOUND. 


FIG.  57. 


beautiful  than  the  last  one,  Fig.  57.  Here  we  have  the 
second  division  of  the  rod,  the  sinuosities  of  which  corre- 
spond to  17^-f  times  its  rate  of  vibra- 
tion as  a  whole.  Thus  every  change  in 
the  sound  of  the  rod  is  accompanied 
by  a  change  of  the  figure  upon  the 
screen. 

The  rate  of  vibration  of  the  rod  as  a 
whole  is  to  the  rate  corresponding  to 
its  first  division  nearly  as  the  square 
of  2  is  to  the  square  of  5,  or  as  4:25.  From  the  first 
division  onward  the  rates  of  vibration  are  approximately 
proportional  to  the  squares  of  the  series  of  odd  numbers 
3,  5,  Y,  9,  11,  etc.  Supposing  the  vibrations  of  the  rod  as 
a  whole  to  number  36,  then  the  vibrations  corresponding 
to  this  and  to  its  successive  divisions  would  be  expressed 
approximately  by  the  following  series  of  numbers: 

36,  225,  625,  1225,  2025,  etc. 
In  Fig.  58,  a,  b,  c,  d,  e,  are  shown  the  modes  of  division 
FIG.  58. 


/ 


corresponding  to  this  series  of  numbers.     You  will  not 
fail  to  observe  that  these  overtones  of  a  vibrating  rod  rise 
far  more  rapidly  in  pitch  than  the  harmonics  of  a  string. 
Other  forms  of  vibration  may  be  obtained  by  smartly 


FIGURES  OF  THE  KALEIDOPHONE.  163 

striking  the  rod  with  the  finger  near  its  fixed  end.  In  fact, 
an  almost  infinite  variety  of  luminous  scrolls  can  be  thus 
produced,  the  beauty  of  which  may  be  inferred  from  the 
subjoined  figures  first  obtained  by  Sir  C.  Wheatstone. 
They  may  be  produced  by  illuminating  the  bead  with  sun- 
light, or  with  the  light  of  a  lamp  or  candle.  The  scrolls, 

FIG.  59. 


moreover,  may  be  doubled  by  employing  two  candles  in- 
stead of  one.     Two  spots  of  light  then  appear,  each  of 


164:  SOUND. 

which  describes  its  own  luminous  line  when  the  knitting- 
needle  is  set  in  vibration.  In  a  subsequent  lecture  we 
shall  become  acquainted  with  "VVheatstone's  application 
of  his  method  to  the  study  of  rectangular  vibrations. 

§  4.  Transverse  Vibrations  of  a  Rod  free  at  Both  Ends. 
The  Claque-bois  and  Glass  Harmonica. 

From  a  rod  or  bar  fixed  at  one  end,  we  will  now  pass 
to  rods  or  bars  free  at  both  ends;  for  such  an  arrangement 
has  also  been  employed  in  music.  By  a  method  afterward 
to  be  described,  Chladni,  the  father  of  modern  acoustics, 
determined  experimentally  the  modes  of  vibration  pos- 
sible to  such  bars.  The  simplest  mode  of  division  in  this 
case  occurs  when  the  rod  is  divided  by  two  nodes  into 
three  vibrating  parts.  This  division  is  easily  illustrated 
by  a  flexible  box  ruler,  six  feet  long.  Holding  it  at  about 
twelve  inches  from  its  two  ends  between  the  forefinger 
and  thumb  of  each  hand,  and  shaking  it,  or  causing  its 
centre  to  be  struck,  it  vibrates,  the  middle  segment  form- 
ing a  shadowy  spindle,  and  the  two  ends  forming  fans. 
The  shadow  of  the  ruler  on  the  screen  renders  the  mode 
of  vibration  very  evident.  In  this  case  the  distance  of 
each  node  from  the  end  of  the  ruler  is  about  one-fourth 

FIG.  60. 


d  — 


of  the  distance  between  the  two  nodes.  In  its  second 
mode  of  vibration  the  rod  or  ruler  is  divided  into  four 
vibrating  parts  by  three  nodes.  In  Fig.  60,  1  and  2, 


THE  CLAQUE-BOIS.  165 

these  respective  modes  of  division  are  shown.  Looking 
at  the  edge  of  the  ruler  1,  the  dotted  lines  cutting  a  a', 
&  &',  show  the  manner  in  which  the  segments  bend  up  and 
down  when  the  first  division  occurs,  while  c  c',  d  d',  show 
the  mode  of  vibration  corresponding  to  the  second  division. 
The  deepest  tone  of  a  rod  free  at  both  ends  is  higher  than 
the  deepest  tone  of  a  rod  fixed  at  one  end  in  the  propor- 
tion of  4:25.  Beginning  with  the  first  two  nodes,  the 
rates  of  vibration  of  the  free  bar  rise  in  the  following  pro- 
portion: 

Number  of  nodes 2,  3,  4,  5,  6,  7. 

Numbers  to  the  squares  of  which  the  )  o    R    n   n    n    10 

r    Oj    0,     4.    €7,    ll.    lo, 

pitch  is  approximately  proportional  ) 

Here,  also,  we  have  a  similarly  rapid  rise  of  pitch  to 
that  noticed  in  the  last  two  cases. 

For  musical  purposes  the  first  division  only  of  a  free 
rod  has  been  employed.  When  bars  of  wood  of  different 
lengths,  widths,  and  depths,  are  strung  along  a  cord  which 
passes  through  the  nodes,  we  have  the  claque-bois  of  the 
French,  an  instrument  now  before  you,  A  B,  Fig.  61.  Sup- 

FIG.  61. 


porting  the  cord  at  one  end  by  a  hook  Tc  and  holding  it  at 
the  other  in  the  left  hand,  I  run  the  hammer  h  along  the 


166 


SOUND. 


series  of  bars,  and  produce  an  agreeable  succession  of  mu- 
sical tones.  Instead  of  using  the  cord,  the  bars  may  rest 
at  their  nodes  on  cylinders  of  twisted  straw;  hence  the 
name  "  straw-fiddle,"  sometimes  applied  to  this  instru- 
ment. Chladni  informs  us  that  it  is  introduced  as  a  play 
of  bells  (Glockenspiel)  into  Mozart's  opera  of  "  Die 
Zauberflb'te."  If,  instead  of  bars  of  wood,  we  employ 
strips  of  glass,  we  have  the  glass  harmonica. 

§  5.   Vibrations  of  a  Tuning-fork. 

From  the  vibrations  of  a  bar  free  at  both  ends,  it  is 
easy  to  pass  to  the  vibrations  of  a  tuning-fork,  as  analyzed 
by  Chladni.  Supposing  a  a,  Fig.  62,  to  represent  a  straight 


steel  bar,  with  the  nodal  points  corresponding  to  its  first 
mode  of  division  marked  by  the  transverse  dots.  Let  the 
bar  be  bent  to  the  form  &  &;  the  two  nodal  points  still  re- 
main, but  they  have  approached  nearer  to  each  other.  The 
tone  of  the  bent  bar  is  also  somewhat  lower  than  that  of 
the  straight  one.  Passing  through  various  stages  of  bend- 
ing, c  c,  d  d,  we  at  length  convert  the  bar  into  a  tuning- 
fork  e  e,  with  parallel  prongs;  it  still  retains  its  two  nodal 
points,  which,  however,  are  much  closer  together  than 
when  the  bar  was  straight. 

When  such  a  fork  sounds  its  deepest  note,  its  free  ends 
oscillate  as  in  Fig.  63,  where  the  prongs  vibrate  between 


NODES  AND  OVERTONES  OF  TUNING-FORK.       167 

the  limits  &  and  n,  and  f  and  m,  and  where  p  and  q  are 
the  nodes.  There  is  no  division  of  a  tuning-fork  corre- 
sponding to  the  division  of  a  straight  bar  by  three  nodes. 
In  its  second  mode  of  division,  which  corresponds  to  the 
first  overtone  of  the  fork,  we  have  a  node  on  each  prong, 
and  two  at  the  bottom.  The  principle  of  Young,  referred 
to  at  p.  145,  extends  also  to  tuning-forks.  To  free  the 
fundamental  tone  from  an  overtone,  you  draw  your  bow 
across  the  fork  at  the  place  where  the  node  is  required  to 
form  the  latter.  In  the  third  mode  of  division  there  are 
two  nodes  on  each  prong  and  one  at  the  bottom.  In  the 
fourth  division  there  are  two  nodes  on  each  prong  and 
two  at  the  bottom;  while  in  the  fifth  division  there  are 
three  nodes  on  each  prong  and  one  at  the  bottom.  The 
first  overtone  of  the  fork  requires,  according  to  Chladni,  6^ 
times  the  number  of  vibrations  of  the  fundamental  tone. 

It  is  easy  to  elicit  the  overtones  of  tuning-forks.  Here, 
for  example,  is  our  old  series,  vibrating  respectively  256, 
320,  384,  and  512  times  in  a  second.  In  passing  from 
the  fundamental  tone  to  the  first  overtone  of  each,  you 
notice  that  the  interval  is  vastly  greater  than  that  between 
the  fundamental  tone  and  the  first  overtone  of  a  stretched 
string.  From  the  numbers  just  mentioned  we  pass  at 
once  to  1,600,  2,000,  2,400,  and  3,200  vibrations  a  second. 
Chladni's  numbers,  however,  though  approximately  cor- 
rect, are  not  always  rigidly  verified  by  experiment.  A  pair 
of  forks,  for  example,  may  have  their  fundamental  tones 
in  perfect  unison  and  their  overtones  discordant.  Two  such 
forks  are  now  before  you.  When  the  fundamental  tones 
of  both  are  sounded,  the  unison  is  perfect;  but  when  the 
first  overtones  of  both  are  sounded,  they  are  not  in  unison. 
You  hear  rapid  "  beats,"  which  grate  upon  the  ear.  By 
loading  one  of  the  forks  with  wax,  the  two  overtones  may 
be  brought  into  unison;  but  now  the  fundamental  tones 
produce  loud  beats  when  sounded  together.  This  could 


168  SOUND. 

not  occur  if  the  first  overtone  of  each  fork  was  produced 
by  a  number  of  vibrations  exactly  6^  times  the  rate  of  its 
fundamental.  In  a  series  of  forks  examined  by  Helmholtz, 
the  number  of  vibrations  of  the  first  overtone  varied  from 
5.6  to  6.6  times  that  of  the  fundamental. 

Starting  from  the  first  overtone,  and  including  it,  the 
rates  of  vibration  of  the  whole  series  of  overtones  are  as 
the  squares  of  the  numbers  3,  5,  7,  9,  etc.  That  is  to  say, 
in  the  time  required  by  the  first  overtone  to  execute  9 
vibrations,  the  second  executes  25,  the  third  49,  the  fourth 
81,  and  so  on.  Thus  the  overtones  of  the  fork  rise  with 
far  greater  rapidity  than  those  of  a  string.  They  also 
vanish  more  speedily,  and  hence  adulterate  to  a  less  extent 
the  fundamental  tone  by  their  admixture. 

§  6.  Chladni's  Figures. 

The  device  of  Chladni  for  rendering  these  sonorous 
vibrations  visible  has  been  of  immense  importance  to  the 
science  of  acoustics.  Lichtenberg  had  made  the  experi- 
ment of  scattering  an  electrified  powder  over  an  electrified 
resin-cake,  the  arrangement  of  the  powder  revealing  the 
electric  condition  of  the  surface.  This  experiment  sug- 
gested to  Chladni  the  idea  of  rendering  sonorous  vibrations 
visible  by  means  of  sand  strewed  upon  the  surface  of  the 
vibrating  body.  Chladni's  own  account  of  his  discovery  is 
of 'sufficient  interest  to  justify  its  introduction  here: 

As  an  admirer  of  music,  the  elements  of  which  I  had 
begun  to  learn  rather  late,  that  is,  in  my  nineteenth  year, 
I  noticed  that  the  science  of  acoustics  was  more  neglected 
than  most  other  portions  of  physics.  This  excited  in  me 
the  desire  to  make  good  the  defect,  and  by  new  discovery 
to  render  some  service  to  this  part  of  science.  In  1785  I 
had  observed  that  a  plate  of  glass  or  metal  gave  different 
sounds  when  it  was  struck  at  different  places,  but  I  could 
nowhere  find  any  information  regarding  the  corresponding 


NODAL  LINES  RENDERED  VISIBLE.  169 

modes  of  vibration.  At  this  time  there  appeared  in  the 
journals  some  notices  of  an  instrument  made  in  Italy  by 
the  Abbe  Mazzochi,  consisting  of  bells,  to  which  one  or 
two  violin-bows  were  applied.  This  suggested  to  me  the 
idea  of  employing  a  violin-bow  to  examine  the  vibrations 
of  different  sonorous  bodies.  When  I  applied  the  bow  to 
a  round  plate  of  glass  fixed  at  its  middle  it  gave  different 
sounds,  which,  compared  with  each  other,  were  (as  regards 
the  number  of  their  vibrations)  equal  to  the  squares  of  2, 
3,  4,  5,  etc. ;  but  the  nature  of  the  motions  to  which  these 
sounds  corresponded,  and  the  means  of  producing  each  of 
them  at  will,  were  yet  unknown  to  me.  The  experiments 
on  the  electric  figures  formed  on  a  plate  of  resin,  dis- 
covered and  published  by  Lichtenberg,  in  the  memoirs  of 
the  Royal  Society  of  Gottingen,  made  me  presume  that 
the  different  vibratory  motions  of  a  sonorous  plate  might 
also  present  different  appearances,  if  a  little  sand  or  some 
other  similar  substance  were  spread  over  the  surface.  On 
employing  this  means,  the  first  figure  that  presented  itself 
to  my  eyes  upon  the  circular  plate  already  mentioned 
resembled  a  star  with  ten  or  twelve  rays,  and  the  very 
acute  sound,  in  the  series  alluded  to,  was  that  which  agreed 
with  the  square  of  the  number  of  diametrical  lines." 

§  7.  Vibrations  of  Square  Plates:  Nodal  Lines. 

I  will  now  illustrate  the  experiments  of  Chladni,  com- 
mencing with  a  square  plate  of  glass  held  by  a  suitable 
clamp  at  its  centre.  The  plate  might  be  held  with  the 
finger  and  thumb,  if  they  could  only  reach  far  enough. 
Scattering  fine  sand  over  the  plate,  the  middle  point  of 
one  of  its  edges  is  damped  by  touching  it  with  the  finger- 
nail, and  a  bow  is  drawn  across  the  edge  of  the  plate,  near 
one  of  its  corners.  The  sand  is  tossed  away  from  certain 
parts  of  the  surface,  and  collects  along  two  nodal  lines 
which  divide  the  large  square  into  four  smaller  ones,  as  in 


170 


SOUND. 


Fig.   64.    -  This  division  of  the  plate  corresponds  to  its 
deepest  tone. 

The  signs  -f  and  —  employed  in  these  figures  denote 
FIG.  64.  FIG.  65. 


FIG.  66. 


that  the  two  squares  on  which  they  occur  are  always  mov- 
ing in  opposite  directions.  When  the  squares  marked  -f 
are  above  the  average  level  of  the  plate  those  marked  — 
are  below  it;  and  when  those  marked  —  are  above  the 
average  level  those  marked  +  are  below  it.  The  nodal 
lines  mark  the  boundaries  of  these  opposing  motions. 
They  are  the  places  of  transition  from  the  one  motion  to 
the  other,  and  are  therefore  unaffected  by  either. 

Scattering  sand  once  more  over  its  surface,  I  damp  one 
of  the  corners  of  the  plate,  and  excite  it  by  drawing  the 
bow  across  the  middle  of  one  of  its  sides.  The  sand 
dances  over  the  surface,  and  finally  ranges  itself  in  two 
sharply-defined  ridges  along  its  diagonals,  Fig.  65.  The 
note  here  produced  is  a  fifth  above  the  last.  Again  damp- 
ing two  other  points,  and  drawing  the  bow  across  the 
centre  of  the  opposite  side  of  the  plate,  we  obtain  a  far 
shriller  note  than  in  either  of  the  former  cases,  and  the 
manner  in  which  the  plate  vibrates  to  produce  this  note  is 
represented  in  Fig.  66. 

Thus  far  plates  of  glass  have  been  employed  held  by  a 
clamp  at  the  centre.  Plates  of  metal  are  still  more  suitable 
for  such  experiments.  Here  is  a  plate  of  brass,  12  inches 
square,  and  supported  on  a  suitable  stand.  Damping  it 


VIBRATIONS  OF  SQUARE  PLATES.  171 

with  the  finger  and  thumb  of  my  left  hand  at  two  points 
of  its  edge,  and  drawing  the  bow  with  my  right  across  a 
vibrating  portion  of  the  opposite  edge,  the  complicated 
pattern  represented  in  Fig.  67  is  obtained. 
FIG.  67. 


The  beautiful  series  of  patterns  shown  on  page  172 
were  obtained  by  Chladni,  by  damping  and  exciting  square 
plates  in  different  ways.  It  is  not  only  interesting  but 
startling  to  see  the  suddenness  with  which  these  sharply- 
defined  figures  are  formed  by  the  sweep  of  the  bow  of  a 
skillful  experimenter. 

§  8.  Wheatstone's  Analysis  of  the  Vibrations  of 
Square  Plates. 

And  now  let  us  look  a  little  more  closely  into  the 
mechanism  of  these  vibrations.  The  manner  in  which  a 
bar  free  at  both  ends  divides  itself  when  it  vibrates  trans- 
versely has  been  already  explained.  Rectangular  pieces 
of  glass  or  of  sheet  metal— the  glass  strips  of  the  har- 
monica, for  example — also  obey  the  laws  of  free  rods  and 
bars.  In  Fig.  69  is  drawn  a  rectangle  a,  with  the  nodes 
corresponding  to  its  first  division  marked  upon  it,  and 
underneath  it  is  placed  a  figure  showing  the  manner  in 


172 


VIBRATIONS  OF  SQUARE  PLATES.  173 

which  the  rectangle,  looked  at  edgeways,  bends  up  and 
down  when  it  is  set  in  vibration.1     For  the  sake  of  plain- 
ness the  bending  is  greatly  exagger-  FIG-  69> 
ated.     The  figures  b  and  c  indicate 
that  the  vibrating  parts  of  the  plate 

alternately  rise  above  and  fall  below    t 

the  average  level  of  the  plate.     At 

one  moment,  for  example,  the  centre    c — ^ r^— — 

of  the  plate  is  above  the  level  and 
its  ends  below  it,  as  at  b;  while  at  the  next  moment  its 
centre  is  below  and  its  two  ends  above  the  average  level, 
as  at  c.  The  vibrations  of  the  plate  consist  in  the  quick 
successive  assumption  of  these  two  positions.  Similar 
remarks  apply  to  all  other  modes  of  division. 

Now  suppose  the  rectangle  gradually  to  widen,  till  it 
becomes  a  square.  There  then  would  be  no  reason  why 
the  nodal  lines  should  form  parallel  to  one  pair  of  sides 
rather  than  to  the  other.  Let  us  now  examine  what  would 
be  the  effect  of  the  coalescence  of  two  such  systems  of 
vibrations. 

To  keep  your  conceptions  clear,  take  two  squares  of 
glass  and  draw  upon  each  of  them  the  nodal  lines  belong- 
ing to  a  rectangle.  Draw  the  lines  on  one  plate  in  white, 
and  on  the  other  in  black;  this  will  help  you  to  keep  the 
plates  distinct  in  your  mind  as  you  look  at  them.  Now 
lay  one  square  upon  the  other  so  that  their  nodal  lines 
shall  coincide,  and  then  realize  with  perfect  mental  clear- 
ness both  plates  in  a  state  of  vibration.  Let  us  assume, 
in  the  first  instance,  that  the  vibrations  of  the  two  plates 
are  concurrent;  that  the  middle  segment  and  the  end  seg- 
ments of  each  rise  and  fall  together;  and  now  suppose  the 

1  I  copy  this  figure  from  Sir  C.  Wheatstone's  memoir;  the  nodes, 
however,  ought  to  be  nearer  the  ends,  and  the  free  terminal  portions  of 
the  dotted  lines  ought  not  to  be  bent  upward  or  downward.  The  nodal 
lines  in  the  next  two  figures  are  also  drawn  too  far  from  the  edge  of 
the  plates. 


174:  SOUND. 

vibrations  of  one  plate  transferred  to  the  other.  What 
would  be  the  result?  Evidently  vibrations  of  a  double 
amplitude  on  the  part  of  the  plate  which  has  received  this 
accession.  But  suppose  the  vibrations  of  the  two  plates, 
instead  of  being  concurrent,  to  be  in  exact  opposition  to 
each  other — that  when  the  middle  segment  of  the  one  rises 
the  middle  segment  of  the  other  falls — what  would  be  the 
consequence  of  adding  them  together?  Evidently  a  neu- 
tralization of  all  vibration. 

Instead  of  placing  the  plates  so  that  their  nodal  lines 
coincide,  set  these  lines  at  right  angles  to  each  other. 
That  is  to  say,  push  A  over  A',  Fig.  TO.  In  these  figures  the 

FIG.  70. 


letter  p  means  positive,  indicating,  in  the  section  where  it 
occurs,  a  motion  of  the  plate  upward ;  while  x  means  nega- 
tive, indicating,  where  it  occurs,  a  motion  downward.  You 
have  now  before  you  a  kind  of  check  pattern,  as  shown  in 
the  third  square,  consisting  of  a  square  s  in  the  middle,  a 
smaller  square  b  at  each  corner,  and  four  rectangles  at  the 
middle  portions  of  the  four  sides.  Let  the  plates  vibrate, 
and  let  the  vibrations  of  their  corresponding  sections  be 
concurrent,  as  indicated  by  the  letters  p  and  x;  and  then 
suppose  the  vibrations  of  one  of  them  transferred  to  the 
other.  What  must  result?  A  moment's  reflection  will 
show  you  that  the  big  middle  square  s  will  vibrate  with 
augmented  energy;  the  same  is  true  of  the  four  smaller 
squares  &,  &,  &,  &,  at  the  four  corners;  but  you  will  at 


ANALYSIS  OF  VIBRATIONS.  175 

once  convince  yourselves  that  the  vibrations  in  the  four 
rectangles  are  in  opposition,  and  that  where  their  ampli- 
tudes are  equal  they  will  destroy  each  other.  The  middle 
point  of  each  side  of  the  plate  of  glass  would,  therefore,  be 
a  point  of  rest;  the  points  where  the  nodal  lines  of  the 
two  plates  cross  each  other  would  also  be  points  of  rest. 
Draw  a  line  through  every  three  of  these  points  and  you 
will  obtain  a  second  square  inscribed  in  the  first.  The 
sides  of  this  square  are  lines  of  no  motion. 

We  have  thus  far  been  theorizing.  Let  us  now  clip 
a  square  plate  of  glass  at  a  point  near  the  centre  of  one 
of  its  edges,  and  draw  the  bow  across  the  adjacent  corner 
of  the  plate.  When  the  glass  is  homogeneous,  a  close 
approximation  to  this  inscribed  square  is  obtained.  The 
reason  is  that  when  the  plate  is  agitated  in  this  manner 
the  two  sets  of  vibrations  which  we  have  been  considering 
actually  coexist  in  the  plate,  and  produce  the  figure  due  to 
their  combination. 

Again,  place  the  squares  of  glass  one  upon  the  other 
exactly  as  in  the  last  case;  but  now,  instead  of  supposing 
them  to  concur  in  their  vibrations,  let  their  corresponding 
sections  oppose  each  other:  that  is,  let  A  cover  A',  Fig.  71. 


Then  it  is  manifest  that  on  superposing  the  vibrations  the 
middle  point  of  our  middle  square  must  be  a  point  of  rest ; 
for  here  the  vibrations  are  equal  and  opposite.  The  inter- 
sections of  ^the  nodal  lines  are  also  points  of  rest,  and 


12 


176  SOUND. 

so  also  is  every  corner  of  the  plate  itself,  for  here  the 
added  vibrations  are  also  equal  and  opposite.  We  have 
thus  fixed  four  points  of  rest  on  each  diagonal  of  the 
square.  Draw  the  diagonals,  and  they  will  represent  the 
nodal  lines  consequent  on  the  superposition  of  the  two 
vibrations. 

These  two  systems  actually  coexist  in  the  same  plate 
when  the  centre  is  clamped  and  one  of  the  corners  touched, 
while  the  fiddle-bow  is  drawn  across  the  middle  of  one  of 
the  sides.  In  this  case  the  sand  which  marks  the  lines  of 
rest  arranges  itself  along  the  diagonals.  This,  in  its  sim- 
plest possible  form,  is  Sir  C.  Wheatstone's  analysis  of  these 
superposed  vibrations. 

§  9.   Vibrations  of  Circular  Plates. 

Passing  from  square  plates  to  round  ones,  we  also 
obtain  various  beautiful  effects.  This  disk  of  brass  is  sup- 
ported horizonally  upon  an  upright  stand:  it  is  black- 
ened, and  fine  white  sand  is  scattered  lightly  over  it.  The 
disk  is  capable  of  dividing  itself  in  various  ways,  and  of 
emitting  notes  of  various  pitch.  I  sound  the  lowest  funda- 
mental note  of  the  disk  by  touching  its  edge  at  a  certain 
point,  and  drawing  the  bow  across  the  edge  at  a  point 
45  degrees  distant  from  the  damped  one.  You  hear  the 
note  and  you  see  the  sand.  It  quits  the  four  quadrants 
of  the  disk,  and  ranges  itself  along  two  of  the  diameters, 
Fig.  72,  A  (next  page).  When  a  disk  divides  itself  thus 
into  four  vibrating  segments,  it  sounds  its  deepest  note.  I 
stop  the  vibration,  clear  the  disk,  and  once  more  scatter 
sand  over  it.  Damping  its  edge,  and  drawing  the  bow 
across  it  at  a  point  30  degrees  distant  from  the  damped 
one,  the  sand  immediately  arranges  itself  in  a  star.  We 
have  here  six  vibrating  segments,  separated  from  each 
other  by  their  appropriate  nodal  lines,  Fig.  72,  B.  Again 
I  damp  a  point,  and  agitate  another  nearer  to  the  damped 


VIBRATIONS  OF  CIRCULAR  PLATES.  177 

one  than  in  the  last  instance;  the  disk  divides  itself  into 
eight  vibrating  segments  with  lines  of  sand  between  them, 
Fig.  72,  c.  In  this  way  the  disk  may  be  subdivided  into 
ten,  twelve,  fourteen,  sixteen  sectors,  the  number  of  sectors 
being  always  an  even  one.  As  the  division  becomes  more 

FIG.  72. 


minute  the  vibrations  become  more  rapid,  and  the  pitch 
consequently  more  high.  The  note  emitted  by  the  sixteen 
segments  into  which  the  disk  is  now  divided  is  so  acute  as 
to  be  almost  painful  to  the  ear.  Here  you  have  Chladni's 
first  discovery.  You  can  understand  his  emotion  on  wit- 
nessing this  wonderful  effect,  "  which  no  mortal  had  pre- 
viously seen."  By  rendering  the  centre  of  the  disk  free, 
and  damping  appropriate  points  of  the  surface,  nodal  cir- 
cles and  other  curved  lines  may  be  obtained. 

The  rate  of  vibration  of  a  disk  is  directly  proportional 
to  its  thickness,  and  inversely  proportional  to  the  square 
of  its  diameter.  Of  these  three  disks  two  have  the  same 
diameter,  but  one  is  twice  as  thick  as  the  other;  two  of 
them  are  of  the  same  thickness,  but  one  has  half  the 
diameter  of  the  other.  According  to  the  law  just  enunci- 
ated, the  rules  of  vibration  of  the  disks  are  as  the  num- 
bers 1,  2,  4.  When  they  are  sounded  in  succession,  the 
musical  ears  present  can  testify  that  they  really  stand  to 
each  other  in  the  relation  of  a  note,  its  octave,  and  its 
double  octave. 


178 


SOUND. 


§  10.  StreliTke  and  Faraday's  Experiments:  Deportment 
of  Light  Powders. 

The  actual  movement  of  the  sand  toward  the  nodal 
lines  may  be  studied  by  clogging  the  sand  with  a  semi-fluid 
substance.  When  gum  is  employed  to  retard  the  motion 
of  the  particles,  the  curves  which  they  individually  de- 
scribe are  very  clearly  drawn  upon  the  plates.  M.  Strehlke 
has  sketched  these  appearances,  and  from  him  the  patterns 
A,  B,  c,  Fig.  73,  are  borrowed. 
FIG.  73. 


An  effect  of  vibrating  plates  which  long  perplexed 
experimenters  is  here  to  be  noticed.  When  with  the  sand 
strewed  over  a  plate  a  little  fine  dust  is  mingled,  say  the 
fine  seed  of  lycopodium,  this  light  substance,  instead  of 
collecting  along  the  nodal  lines,  forms  little  heaps  at  the 
places  of  most  violent  motion.  It  is  heaped  at  the  four 
corners  of  the  plate,  Fig.  74,  at  the  four  sides  of  the  plate, 

FIG.  74.  FIG.  75.  FIG.  76. 


Fig.  75,  and  lodged  between  the  nodal  lines  of  the  plate, 


VIBKATIONS  OF  BELLS.  179 

Fig.  76.  These  three  figures  represent  the  three  states  of 
vibration  illustrated  in  Figs.  64,  65,  and  66.  The  dust 
chooses  in  all  cases  the  place  of  greatest  agitation.  Vari- 
ous explanations  of  this  effect  had  been  given,  but  it  was 
reserved  for  Faraday  to  assign  its  extremely  simple  cause. 
The  light  powder  is  entangled  by  the  little  whirlwinds  of 
air  produced  by  the  vibrations  of  the  plate:  it  cannot 
escape  from  the  little  cyclones,  though  the  heavier  sand 
particles  are  readily  driven  through  them.  When,  there- 
fore, the  motion  ceases,  the  light  powder  settles  down  at 
the  places  where  the  vibration  was  a  maximum.  In  vacuo 
no  such  effect  is  observed:  here  all  powders,  light  and 
heavy,  move  to  the  nodal  lines. 

§  11.   Vibration  of  Bells:  Means  of  rendering 
them  visible. 

The  vibrating  segments  and  nodes  of  a  bell  are  similar 
to  those  of  a  disk.  When  a  bell  sounds  its  deepest  note, 
the  coalescence  of  its  pulses  causes  it  to  divide  into  four 
vibrating  segments,  separated  from  each  other  by  four 
nodal  lines,  which  run  up  from  the  sound-bow  to  the 
crown  of  the  bell.  The  place  where  the  hammer  strikes  is 
always  the  middle  of  a  vibrating  segment;  the  point  dia- 
metrically opposite  is  also  the  middle  of  such  a  segment. 
Ninety  degrees  from  these  points,  we  have  also  vibrating 
segments,  while  at  45  degrees  right  and  left  of  them  we 
come  upon  the  nodal  lines.  Supposing  the  strong,  dark 
circle  in  Fig.  77  (next  page)  to  represent  the  circumference 
of  the  bell  in  a  state  of  quiescence,  then  when  the  ham- 
mer falls  on  any  one  of  the  segments  a,  c,  6,  or  d,  the  sound- 
bow  passes  periodically  through  the  changes  indicated  by 
the  dotted  lines.  At  one  moment  it  is  an  oval,  with  a  b 
for  its  longest  diameter;  at  the  next  moment  it  is  an  oval, 
with  c  d  for  its  longest  diameter.  The  changes  from  one 
oval  to  the  other  constitute,  in  fact,  the  vibrations  of 


180  SOUND. 

the  bell.  The  four  points  n,  n,  n,  n,  where  the  two  ovals 
intersect  each  other,  are  the  nodes.  As  in  the  case  of 
a  disk,  the  number  of  vibra- 
tions executed  by  a  bell  in  a 
given  time  varies  directly  as 
the  thickness,  and  inversely  as 
the  square  of  the  bell's  diam- 
eter. 

Like  a  disk,  also,  a  bell  can 
divide  itself  into  any  even  num- 
ber of  vibrating  segments,  but 
not  into  an  odd  number.  By  ~ii 

damping  proper  points  in  suc- 
cession the  bell  can  be  caused  to  divide  into  6,  8,  10,  and 
12  vibrating  parts.  Beginning  with  the  fundamental  note, 
the  number  of  vibrations  corresponding  to  the  respective 
divisions  of  a  bell,  as  of  a  disk,  is  as  follows: 

Number  of  divisions 4,  6,  8,  10,  12. 

Numbers  the  squares  of  which  express  j.  3   3   4   5   6 
the  rates  of  vibration       .        .        .       )     ' 

Thus,  if  the  vibrations  of  the  fundamental  tone  be  40, 
that  of  the  next  higher  tone  will  be  90,  the  next  160,  the 
next  250,  the  next  360,  and  so  on.  If  the  bell  be  thin, 
the  tendency  to  subdivision  is  so  great,  that  it  is  almost 
impossible  to  bring  out  the  pure  fundamental  tone  without 
the  admixture  of  the  higher  ones. 

I  will  now  repeat  before  you  a  homely,  but  an  instruc- 
tive experiment.  This  common  jug,  when  a  fiiddle-bow  is 
drawn  across  its  edge,  divides  into  four  vibrating  segments 
exactly  like  a  bell.  The  jug  is  provided  with  a  handle; 
and  you  are  to  notice  the  influence  of  this  handle  upon  the 
tone.  When  the  fiddle-bow  is  drawn  across  the  edge  at  a 
point  diametrically  opposite  to  the  handle,  a  certain  note  is 
heard.  When  it  is  drawn  at  a  point  90°  from  the  handle, 
the  same  note  is  heard.  In  both  these  cases  the  handle 


SONOROUS  RIPPLES.  181 

occupies  the  middle  of  a  vibrating  segment,  loading  that 
segment  by  its  weight.  But  I  now  draw  the  bow  at  an  an- 
gular distance  of  45  from  the  handle;  the  note  is  sensibly 
higher  than  before.  The  handle  in  this  experiment  occu- 
pies a  node;  it  no  longer  loads  a  vibrating  segment,  and 
hence  the  elastic  force,  having  to  cope  with  less  weight, 
produces  a  more  rapid  vibration.  Chladni  executed  with 
a  teacup  the  experiment  here  made  with  a  jug.  Now  bells 
often  exhibit  round  their  sound-bows  an  absence  of  uni- 
form thickness,  tantamount  to  the  want  of  symmetry  in 
the  case  of  our  jug;  and  we  shall  learn  subsequently  that 
the  intermittent  sound  of  many  bells,  noticed  more  par- 
ticularly when  their  tones  are  dying  out,  is  produced  by 
the  combination  of  two  distinct  rates  of  vibration,  which 
have  this  absence  of  uniformity  for  their  origin. 

There  are  no  points  of  absolute  rest  in  a  vibrating  bell, 
for  the  nodes  of  the  higher  tones  are  not  those  of  the  fun- 
damental one.  But  it  is  easy  to  show  that  the  various 
parts  of  the  sound-bow,  when  the  fundamental  tone  is  pre- 
dominant, vibrate  with  very  different  degrees  of  intensity. 
Suspending  a  little  ball  of  sealing-wax  a,  Fig.  78  (next 
page),  by  a  string,  and  allowing  it  to  rest  gently  against 
the  interior  surface  of  an  inverted  bell,  it  is  tossed  to  and 
fro  when  the  bell  is  thrown  into  vibration.  But  the  rat- 
tling of  the  sealing-wax  ball  is  far  more  violent  when  it 
rests  against  the  vibrating  segments  than  when  it  rests 
against  the  nodes.  Permitting  the  ivory  bob  of  a  short 
pendulum  to  rest  in  succession  against  a  vibrating  segment 
and  against  a  node  of  the  "  Great  Bell  "  of  Westminster,  I 
found  that  in  the  former  position  it  was  driven  away  five 
inches,  in  the  latter  only  two  inches  and  three-quarters, 
when  the  hammer  fell  upon  the  bell. 

Could  the  "  Great  Bell "  be  turned  upside  down  and 
filled  with  water,  on  striking  it  the  vibrations  would 
express  themselves  in  beautiful  ripples  upon  the  liquid 


182 


SOUND. 


surface.  Similar  ripples  may  be  obtained  with  smaller 
bells,  or  even  with  finger  and  claret  glasses,  but  they 
would  be  too  minute  for  our  present  purpose.  Filling  a 
large  hemispherical  glass  with  water,  and  passing  the 
fiddle-bow  across  its  edge,  large  crispations  immediately 
cover  its  surface.  When  the  bow  is  vigorously  drawn,  the 
water  rises  in  spray  from  the  four  vibrating  segments. 
Projecting,  by  means  of  a  lens,  a  magnified  image  of  the 


FIG.  78. 


illuminated  water-surface  upon  the  screen,  I  pass  the  bow 
gently  across  the  edge  of  the  glass,  or  rub  the  finger  gently 
along  the  edge.  You  hear  this  low  sound,  and  at  the  same 
time  observe  the  ripples  breaking,  as  it  were,  in  visible 
music  over  the  four  sectors  of  the  figure. 

You  know  the  experiment  of  Leidenfrost  which  proves 
that,  if  water  be  poured  into  a  red-hot  silver  basin,  it  rolls 
about  upon  its  own  vapor.  The  same  effect  is  produced 
if  we  drop  a  volatile  liquid,  like  ether,  on  the  surface  of 
warm  water.  And,  if  a  bell-glass  be  filled  with  ether  or 


FARADAY'S  AND  MELDE'S  FIGURES. 


183 


with  alcohol,  a  sharp  sweep  of  the  bow  over  the  edge  of 
the  glass  detaches  the  liquid  spherules,  which,  when  they 
fall  back,  do  not  mix  with  the  liquid,  but  are  driven  over 
the  surface  on  wheels  of  vapor  to  the  nodal  lines.  The 
warming  of  the  liquid,  as  might  be  expected,  improves  the 
effect.  M.  Melde,  to  whom  we  are  indebted  for  this  beau- 
tiful experiment,  has  given  the  drawings,  Figs.  79  and  80, 


FIG.  79. 


FIG.  80. 


representing  what  occurs  when  the  surface  is  divided  into 
four  and  into  six  vibrating  parts.  "With  a  thin  wine-glass 
and  strong  brandy  the  effect  may  also  be  obtained.1 

The  glass  and  the  liquid  within  it  vibrate  here  to- 
gether, and  everything  that  interferes  with  the  perfect 
continuity  of  the  entire  mass  disturbs  the  sonorous  effect. 
A  crack  in  the  glass  passing  from  the  edge  downward  ex- 
tinguishes its  sounding  power.  A  rupture  in  the  continu- 
ity of  the  liquid  has  the  same  effect.  When  a  glass  con- 
taining a  solution  of  carbonate  of  soda  is  struck  with  a 
bit  of  wood,  you  hear  a  clear  musical  sound.  But  when  a 
little  tartaric  acid  is  added  to  the  liquid,  it  foams,  and  a 

1  Under  the  shoulder  of  the  Wetterhorn  I  found  in  1867  a  pool  of 
clear  water  into  which  a  driblet  fell  from  a  brow  of  overhanging  lime- 
stone rock.  The  rebounding  water-drops,  when  they  fell  back,  rolled 
in  myriads  over  the  surface.  Almost  any  fountain,  the  spray  of  which 
falls  into  a  basin,  will  exhibit  the  same  effect. 


184 


SOUND. 


FIG.  81. 


dry,  unmusical  collision  takes  the  place  of  the  musical 
sound.  As  the  foam  disappears,  the  sonorous  power  re- 
turns, and  now  that  the  liquid  is  once  more  clear,  YOU 
hear  the  musical  ring  as  before. 

The  ripples  of  the  tide  leave  their  impressions  upon 
the  sand  over  which  they  pass. 
The  ripples  produced  by  so- 
norous vibrations  have  been 
proved  by  Faraday  competent 
to  do  the  same.  Attaching  a 
plate  of  glass  to  a  long  flexible 
board,  and  pouring  a  thin  layer 
of  water  over  the  surface  of 
the  glass,  on  causing  the  board 
to  vibrate,  its  tremors  chase 
the  water  into  a  beautiful  mo- 


saic of  ripples.  A  thin  stratum  of  sand  strewed  upon  the 
plate  is  acted  upon  by  the  water,  and  carved  into  patterns, 
of  which  Fig.  81  is  a  reduced  specimen. 


SUMMARY.  185 


SUMMARY  OF  CHAPTER  IV. 

A  ROD  fixed  at  both  ends  and  caused  to  vibrate  trans- 
versely divides  itself  in  the  same  manner  as  a  string  vibrat- 
ing transversely. 

But  the  succession  of  its  overtones  is  not  the  same  as 
those  of  a  string,  for  while  the  series  of  tones  emitted  by 
the  string  is  expressed  by  the  natural  numbers,  1,  2,  3,  4, 
5,  etc.,  the  series  of  tones  emitted  by  the  rod  is  expressed 
by  the  squares  of  the  odd  numbers,  3,  5,  7,  9,  etc. 

A  rod  fixed  at  one  end  can  also  vibrate  as  a  whole,  or 
can  divide  itself  into  vibrating  segments  separated  from 
each  other  by  nodes. 

In  this  case  the  rate  of  vibration  of  the  fundamental 
tone  is  to  that  of  the  first  overtone  as  4 :  25,  or  as  the 
square  of  2  to  the  square  of  5.  From  the  first  division  on- 
ward the  rates  of  vibration  are  proportional  to  the  squares 
of  the  odd  numbers,  3,  5,  7,  9,  etc. 

With  rods  of  different  lengths  the  rate  of  vibration  is 
inversely  proportional  to  the  square  of  the  length  of  the 
rod. 

Attaching  a  glass  bead  silvered  within  to  the  free  end 
of  the  rod,  and  illuminating  the  bead,  the  spot  of  light  re- 
flected from  it  describes  curves  of  various  forms  wrhen  the 
rod  vibrates.  The  kaleidophone  of  Wheatstone  is  thus 
constructed. 

The  iron  fiddle  and  the  musical  box  are  instruments 
whose  tones  are  produced  by  rods,  or  tongues,  fixed  at  one 
end  and  free  at  the  other. 

A  rod  free  at  both  ends  can  also  be  rendered  a  source 


186  SOUND. 

of  sonorous  vibrations.  In  its  simplest  mode  of  division 
it  has  two  nodes,  the  subsequent  overtones  correspond  to 
divisions  by  3,  4,  5,  etc.,  nodes.  Beginning  with  its  first 
mode  of  division,  the  tones  of  such  a  rod  are  represented 
by  the  squares  of  the  odd  numbers  3,  5,  7,  9,  etc. 

The  claque-bois,  straw-fiddle,  and  glass  harmonica  are 
instruments  whose  tones  are  those  of  rods  or  bars  free  at 
both  ends,  and  supported  at  their  nodes. 

When  a  straight  bar,  free  at  both  ends,  is  gradually 
bent  at  its  centre,  the  two  nodes  corresponding  to  its  fun- 
damental tone  gradually  approach  each  other.  It  finally 
assumes  the  shape  of  a  tuning-fork  which,  when  it  sounds 
its  fundamental  note,  is  divided  by  two  nodes  near  the 
base  of  its  two  prongs  into  three  vibrating  parts. 

There  is  no  division  of  a  tuning-fork  by  three  nodes. 

In  its  second  mode  of  division,  which  corresponds  to 
the  first  overtone  of  the  fork,  there  is  a  node  on  each 
prong  and  two  others  at  the  bottom  of  the  fork. 

The  fundamental  tone  of  the  fork  is  to  its  first  over- 
tone approximately  as  the  square  of  2  is  to  the  square  of  5. 
The  vibrations  of  the  first  overtone  are,  therefore,  about 
6^  times  as  rapid  as  those  of  the  fundamental.  From  the 
first  overtone  onward  the  successive  rates  of  vibration  are 
as  the  squares  of  the  odd  numbers  3,  5,  7,  9,  etc. 

We  are  indebted  to  Chladni  for  the  experimental  in- 
vestigation of  all  these  points.  He  was  enabled  to  con- 
duct his  inquiries  by  means  of  the  discovery  that,  when 
sand  is  scattered  over  a  vibrating  surface,  it  is  driven  from 
the  vibrating  portions  of  the  surface,  and  collects  along 
the  nodal  lines. 

Chladni  embraced  in  his  investigations  plates  of  vari- 
ous forms.  A  square  plate,  for  example,  clamped  at  the 
centre,  and  caused  to  emit  its  fundamental  tone,  divides 
itself  into  four  smaller  squares  by  lines  parallel  to  its 
sides. 


SUMMARY.  187 

The  same  plate  can  divide  itself  into  four  triangular 
vibrating  parts,  the  nodal  lines  coinciding  with  the  diag- 
onals. The  note  produced  in  this  case  is  a  fifth  above 
the  fundamental  note  of  the  plate. 

The  plate  may  be  further  subdivided,  sand-figures  of 
extreme  beauty  being  produced;  the  notes  rise  in  pitch  as 
the  subdivision  of  the  plate  becomes  more  minute. 

These  figures  may  be  deduced  from  the  coalescence  of 
different  systems  of  vibration. 

When  a  circular  plate  clamped  at  its  centre  sounds  its 
fundamental  tone,  it  divides  into  four  vibrating  parts, 
separated  by  four  radial  nodal  lines. 

The  next  note  of  the  plate  corresponds  to  a  division 
into  six  vibrating  sectors,  the  next  note  to  a  division  into 
eight  sectors;  such  a  plate  can  divide  into  any  even 
number  of  vibrating  sectors,  the  sand-figures  assuming 
beautiful  stellar  forms. 

The  rates  of  vibration  corresponding  to  the  divisions 
of  a  disk  are  represented  by  the  squares  of  the  numbers 
2,  3,  4,  5,  6,  etc.  In  other  words,  the  rates  of  vibration 
are  proportional  to  the  squares  of  the  numbers  represent- 
ing the  sectors  into  which  the  disk  is  divided. 

When  a  bell  sounds  its  deepest  note  it  is  divided  into 
four  vibrating  parts  separated  from  each  other  by  nodal 
lines,  which  run  upward  from  the  sound-bow  and  cross 
each  other  at  the  crown. 

It  is  capable  of  the  same  subdivisions  as  a  disk;  the 
succession  of  its  tones  being  also  the  same. 

The  rate  of  vibration  of  a  disk  or  bell  is  directly  pro- 
portional to  the  thickness  and  inversely  proportional  to 
the  square  of  the  diameter. 


CHAPTEE  V. 

Longitudinal  Vibrations  of  a  Wire.— Relative  Velocities  of  Sound  in 
Brass  and  Iron. — Longitudinal  Vibrations  of  Rods  fixed  at  One 
End. — Of  Rods  free  at  Both  Ends. — Divisions  and  Overtones  of 
Rods  vibrating  longitudinally.— Examination  of  Vibrating  Bars  by 
Polarized  Light. — Determination  of  Velocity  of  Sound  in  Solids. — 
Resonance. — Vibrations  of  Stopped  Pipes:  their  Divisions  and 
Overtones. — Relation  of  the  Tones  of  Stopped  Pipes  to  those  of 
Open  Pipes. — Condition  of  Column  of  Air  within  a  Sounding 
Organ-Pipe. — Reeds  and  Reed-Pipes. — The  Voice. — Overtones  of 
the  Vocal  Chords. — The  Vowel  Sounds. — Kundt's  Experiments. — 
New  Methods  of  determining  the  Velocity  of  Sound. 

§  1.  Longitudinal  Vibrations  of  Wires  and  Rods:  Con- 
version of  Longitudinal  into  Transverse  Vibrations. 

WE  have  thus  far  occupied  ourselves  exclusively  with 
transversal  vibrations;  that  is  to  say,  vibrations  executed 
at  right  angles  to  the  lengths  of  the  strings,  rods,  plates, 
and  bells  subjected  to  examination.  A  string  is  also 
capable  of  vibrating  in  the  direction  of  its  length,  but 
here  the  power  which  enables  it  to  vibrate  is  not  a  ten- 
sion applied  externally,  but  the  elastic  force  of  its  own 
molecules.  Now  this  molecular  elasticity  is  much  greater 
than  any  that  we  can  ordinarily  develop  by  stretching  the 
string,  and  the  consequence  is  that  the  sounds  produced 
by  the  longitudinal  vibrations  of  a  string  are,  as  a  gen- 
eral rule,  much  more  acute  than  those  produced  by  its 
transverse  vibrations.  These  longitudinal  vibrations  may 
be  excited  by  the  oblique  passage  of  a  fiddle-bow;  but 
they  are  more  easily  produced  by  passing  briskly  along 
the  string  a  bit  of  cloth  or  leather  on  which  powdered 
188 


LONGITUDINAL  VIBRATIONS  OF  WIRES.  189 

resin  has  been  strewed.  The  resined  fingers  answer  the 
same  purpose. 

When  the  wire  of  our  monochord  is  plucked  aside,  you 
hear  the  sound  produced  by  its  transverse  vibrations. 
When  resined  leather  is  rubbed  along  the  wire,  a  note 
much  more  piercing  than  the  last  is  heard.  This  is  due 
to  the  longitudinal  vibrations  of  the  wire.  Behind  the 
table  is  stretched  a  stout  iron  wire,  23  feet  long.  One  end 
of  it  is  firmly  attached  to  an  immovable  wooden  tray, 
the  other  end  is  coiled  round  a  pin  fixed  firmly  into  one 
of  our  benches.  With  a  key  this  pin  can  be  turned,  and 
the  wire  stretched  so  as  to  facilitate  the  passage  of  the 
rubber.  Clasping  the  wire  with  the  resined  leather,  and 
passing  the  hand  to  and  fro  along  it,  a  rich,  loud  musical 
sound  is  heard.  Halving  the  wire  at  its  centre,  and 
rubbing  one  of  its  halves,  the  note  heard  is  the  octave  of 
the  last:  the  vibrations  are  twice  as  rapid.  When  the 
wire  is  clipped  at  one-third  of  its  length  and  the  shorter 
segment  rubbed,  the  note  is  a  fifth  above  the  octave. 
Taking  one-fourth  of  its  length  and  rubbing  as  before,  the 
note  yielded  is  the  double  octave  of  that  of  the  whole  wire, 
being  produced  by  four  times  the  number  of  vibrations. 
Thus,  in  longitudinal  as  well  as  in  transverse  vibrations, 
the  number  of  vibrations  executed  in  a  given  time  is 
inversely  proportional  to  the  length  of  the  wire. 

And  notice  the  surprising  power  of  these  sounds  when 
the  ware  is  rubbed  vigorously.  With  a  shorter  length, 
the  note  is  so  acute,  and  at  the  same  time  so  powerful,  as 
to  be  hardly  bearable.  It  is  not  the  wire  itself  which 
produces  this  intense  sound;  it  is  the  wooden  tray  at  its 
end  to  which  its  vibrations  are  communicated.  And,  the 
vibrations  of  the  wire  being  longitudinal,  those  of  the 
tray,  which  is  at  right  angles  to  the  wire,  must  be  trans- 
versal. We  have  here,  indeed,  an  instructive  example  of 
the  conversion  of  longitudinal  into  transverse  vibrations. 


190  SOUND. 

§  2.  Longitudinal  Pulses  in  Iron  and  Brass :  their  Rela- 
tive Velocities  determined. 

Causing  the  wire  to  vibrate  again  longitudinally 
through  its  entire  length,  my  assistant  shall  at  the  same 
time  turn  the  key  at  the  end,  thus  changing  the  tension. 
You  notice  no  variation  of  the  note.  The  longitudinal 
vibrations  of  the  wire,  unlike  the  transverse  ones,  are  in- 
dependent of  the  tension.  Beside  the  iron  wire  is  stretched 
a  second,  of  brass,  of  the  same  length  and  thickness.  I 
rub  them  both.  Their  tones  are  not  the  same;  that  of 
the  iron  wire  is  considerably  the  higher  of  the  two.  Why? 
Simply  because  the  velocity  of  the  sound-pulse  is  greater 
in  iron  than  in  brass.  The  pulses  in  this  case  pass  to  and 
fro  from  end  to  end  of  the  wire.  At  one  moment  the  wire 
pushes  the  tray  at  its  end;  at  the  next  moment  it  pulls 
the  tray,  this  pushing  and  pulling  being  due  to  the 
passage  of  the  pulse  to  and  fro  along  the  whole  wire.  The 
time  required  for  a  pulse  to  run  from  one  end  to  the  other 
and  back  is  that  of  a  complete  vibration.  In  that  time 
the  wire  imparts  one  push  and  one  pull  to  the  wooden 
tray  at  its  end;  the  wooden  tray  imparts  one  complete 
vibration  to  the  air,  and  the  air  bends  once  in  and  once 
out  the  tympanic  membrane.  It  is  manifest  that  the 
rapidity  of  vibration,  or,  in  other  words,  the  pitch  of  the 
note,  depends  upon  the  velocity  with  which  the  sound- 
pulse  is  transmitted  through  the  wire. 

And  now  the  solution  of  a  beautiful  problem  falls  of 
itself  into  our  hands.  By  shortening  the  brass  wire  we 
cause  it  to  emit  a  note  of  the  same  pitch  as  that  emitted 
by  the  other.  You  hear  both  notes  now  sounding  in 
unison,  and  the  reason  is  that  the  sound-pulse  travels 
through  these  23  feet  of  iron  wire,  and  through  these 
15  feet  6  inches  of  brass  wire,  in  the  same  time.  These 
lengths  are  in  the  ratio  of  11 :  17,  and  these  two  numbers 


LONGITUDINAL  VIBRATIONS  OF  WIRES.  191 

express  the  relative  velocities  of  sound  in  brass  and  iron. 
In  fact,  the  former  velocity  is  11,000  feet,  and  the  latter 
17,000  feet  a  second.  The  same  method  is  of  course  ap- 
plicable to  many  other  metals. 

When  a  wire  or  string,  vibrating  longitudinally,  emits 
its  lowest  note,  there  is  no  node  whatever  upon  it;  the 
pulse,  as  just  stated,  runs  to  and  fro  along  the  whole 
length.  But,  like  a  string  vibrating  transversely,  it  can 
also  subdivide  itself  into  ventral  segments  separated  by 
nodes.  By  damping  the  centre  of  the  wire  we  make  that 
point  a  node.  The  pulses  here  run  from  both  ends,  meet 
in  the  centre,  recoil  from  each  other,  and  return  to  the 
ends,  where  they  are  reflected  as  before.  The  note  pro- 
duced is  the  octave  of  the  fundamental  note.  The  next 
higher  note  corresponds  to  the  division  of  the  wire  into 
three  vibrating  segments,  separated  from  each  other  by 
two  nodes.  The  first  of  these  three  modes  of  vibration  is 
shown  in  Fig.  82,  a  and  b;  the  second  at  c  and  d;  the 
FIG.  82. 


I 


pt-E — |  v*  ; — ±^4    |-:± — i  ^r    I    -±^| 

third  at  e  and  f;  the  nodes  being  marked  by  dotted  trans- 
verse lines,  and  the  arrows  in  each  case  pointing  out  the 
direction  in  which  the  pulse  moves.  The  rates  of  vibra- 
tion follow  the  order  of  the  numbers,  1,  2,  3,  4,  5,  etc., 
just  as  in  the  case  of  a  wire  vibrating  transversely. 

A  rod  or  bar  of  wood  or  metal,  with  its  two  ends  fixed, 
and  vibrating  longitudinally,  divides  itself  in  the  same 
manner  as  the  wire.     The  succession  of  tones  is  also  the 
same  in  both  cases. 
J3 


192 


SOUND. 


§  3.  Longitudinal  Vibrations  of  Rods  fixed  at  One  End: 
Musical  Instruments  formed  on  this  Principle. 

Rods  and  bars  with  one  end  fixed  are  also  capable  of 
vibrating  longitudinally.  A  smooth  wooden  or  metal  rod, 
for  example,  with  one  of  its  ends  fixed  in  a  vice,  yields  a 
musical  note,  when  the  resined  fingers  are  passed  along  it. 
When  such  a  note  yields  its  lowest  note,  it  simply  elon- 
gates and  shortens  in  quick  alternation;  there  is,  then, 
no  node  upon  the  rod.  The  pitch  of  the  note  is  inversely 
proportional  to  the  length  of  the  rod.  This  follows  neces- 
sarily from  the  fact  that  the  time  of  a  complete  vibration 
is  the  time  required  for  the  sonorous  pulse  to  run  twice  to 
and  fro  over  the  rod.  The  first  overtone  of  a  rod,  fixed  at 
one  end,  corresponds  to  its  division  by  a  node  at  a  point 
one-third  of  its  length  from  its  free  end.  Its  second  over- 
tone corresponds  to  a  division  by  two  nodes,  the  highest 
of  which  is  at  a  point  one-fifth  of  the  length  of  the  rod 
from  its  free  end,  the  remainder  of  the  rod  being  divided 
into  two  equal  parts  by  the  second  node.  In  Fig.  83,  a  and 
FlG  83  6,  c  and  d,  e  and  f,  are 

shown  the  conditions  of 
the  rod  answering  to  its 
first  three  modes  of  vibra- 
tion: the  nodes,  as  before, 
are  marked  by  dotted 
lines,  the  arrows  in  the 
respective  cases  mark- 
ing the  direction  of  the 
pulses. 

The  order  of  the  tones  of  a  rod  fixed  at  one  end  and 
vibrating  longitudinally  is  that  of  the  odd  numbers  1,  3, 
5,  7,  etc.  It  is  easy  to  see  that  this  must  be  the  case. 
For  the  time  of  vibration  of  c  or  d  is  that  of  the  segment 
above  the  dotted  line:  and  the  length  of  this  segment 


i 

M 

-     - 

! 

1    1 

I 

•  • 

a 

6         c 

d 

•     • 

•  • 

LONGITUDINAL  VIBRATIONS  OF  FIXED  KODS.     193 


Fia.  84. 


being  only  one-third  that  of  the  whole  rod,  its  vibrations 
must  be  three  times  as  rapid.  The  time  of  vibration  in 
e  or  /  is  also  that  of  its 
highest  segment,  and  as 
this  segment  is  one-fifth 
of  the  length  of  the 
whole  rod,  its  vibrations 
must  be  five  times  as 
rapid.  Thus  the  order 
of  the  tones  must  be 
that  of  the  odd  numbers. 
Before  you,  Fig.  84, 
is  a  musical  instrument, 
the  sounds  of  which  are 
due  to  the  longitudinal 
vibrations  of  a  number 
of  deal  rods  of  different 
lengths.  Passing  the  res- 
ined  fingers  over  the  rods 
in  succession,  a  series  of 
notes  of  varying  pitch  is 
obtained.  An  expert  per- 
former might  render  the 
tones  of  this  instrument  very  pleasant  to  you. 

§  4.   Vibrations  of  Rods  free  at  Both  Ends. 

Rods  with  both  ends  free  are  also  capable  of  vibrating 
longitudinally,  and  producing  musical  tones.  The  investi- 
gation of  this  subject  will  lead  us  to  exceedingly  important 
results.  Clasping  a  long  glass  tube  exactly  at  its  centre, 
and  passing  a  wetted  cloth  over  one  of  its  halves,  a  clear 
musical  sound  is  the  result.  A  solid  glass  rod  of  the  same 
length  would  yield  the  same  note.  In  this  case  the  centre 
of  the  tube  is  a  node,  and  the  two  halves  elongate  and 
shorten  in  quick  alternation.  M.  Konig,  of  Paris,  has  pro- 


194 


SOUND. 


vided  us  with  an  instrument  which  will  illustrate  this 
action.  A  rod  of  brass,  a  &,  Fig.  85,  is  held  at  its  centre 
by  the  clamp  s,  while  an  ivory  ball,  suspended  by  two 
strings  from  the  points,  m  and  n,  of  a  wooden  frame,  is 
caused  to  rest  against  the  end,  6,  of  the  brass  rod.  Draw- 
ing gently  a  bit  of  resined  leather  over  the  rod  near  a,  it 
is  thrown  into  longitudinal  vibration.  The  centre,  s,  is  a 
node;  but  the  uneasiness  of  the  ivory  ball  shows  you  that 
the  end,  &,  is  in  a  state  of  tremor.  I  apply  the  rubber 
still  more  briskly.  The  ball,  6,  rattles,  and  now  the  vi- 


FIG.  85. 


bration  is  so  intense,  that  the  ball  is  rejected  with  vio- 
lence whenever  it  comes  into  contact  with  the  end  of  the 
rod. 

§  5.  Fracture  of  Glass  Tube  ~by  Sonorous 
Vibrations. 

"When  the  wetted  cloth  is  passed  over  the  surface  of 
a  glass  tube  the  film  of  liquid  left  behind  by  the  cloth 
is  seen  forming  narrow  tremulous  rings  all  along  the  rod. 
Now  this  shivering  of  the  liquid  is  due  to  the  shivering  of 
the  glass  underneath  it,  and  it  is  possible  so  to  augment 
the  intensity  of  the  vibration  that  the  glass  shall  actually 
go  to  pieces.  Savart  was  the  first  to  show  this.  Twice 


LONGITUDINAL  VIBRATIONS  OF  FREE  RODS.     195 


FIG.  87. 


in  this  place  I  have  repeated  this  experiment,  sacrificing 
in  each  case  a  fine  glass  tube  6  feet  long  and  2  inches  in 
diameter.  Seizing  the  tube  at  its  centre  c,  Fig.  86,  I 
swept  my  hand  vigorously  to  and  fro  along  c  D,  until 
finally  the  half  most 
distant  from  my  hand 
was  shivered  into  an- 
nular fragments.  On 
examining  these  it  was 
found  that,  narrow  as 
they  were,  many  of 
them  were  marked  by 
circular  cracks  indi- 
cating a  still  more 
minute  subdivision. 

In  this  case  also 
the  rapidity  of  vibra- 
tion is  inversely  pro- 
portional to  the  length 
of  the  rod.  A  rod 
of  half  the  length  vi- 
brates longitudinally 
with  double  the  ra- 
pidity, a  rod  of  one- 
third  the  length  with 
treble  the  rapidity,  and 
so  on.  The  time  of 
a  complete  vibration 
being  that  required 
by  the  pulse  to  travel 
to  and  fro  over  the 
rod,  and  that  time 
being  directly  propor- 
tional to  the  length  of  the  rod,  the  rapidity  of  vibration 
must,  of  necessity,  be  in  the  inverse  proportion. 


a 


196  SOUND. 

This  division  of  a  rod  by  a  single  node  at  its  centre 
corresponds  to  the  deepest  tone  produced  by  its  longi- 
tudinal vibration.  But,  as  in  all  other  cases  hitherto 
examined,  such  rods  can  subdivide  themselves  further. 
Holding  the  long  glass  rod  a  e,  Fig.  87,  at  a  point  &,  mid- 
way between  its  centre  and  one  of  its  ends,  and  rubbing 
its  short  section,  a  &,  with  a  wet  cloth,  the  point  b  be- 
comes a  node,  a  second  node,  d,  being  formed  at  the  same 
distance  from  the  opposite  end  of  the  rod.  Thus  we  have 
the  rod  divided  into  three  vibrating  parts,  consisting  of 
one  whole  ventral  segment,  b  d,  and  two  half  ones,  a  b 
and  d  e.  The  sound  corresponding  to  this  division  of  the 
rod  is  the  octave  of  its  fundamental  note. 

You  have  now  a  means  of  checking  me.  For,  if  the 
second  mode  of  division  just  described  produces  the  octave 
of  the  fundamental  note,  and  if  a  rod  of  half  the  length 
produces  the  same  octave,  then  the  whole  rod  held  at  a 
point  one-fourth  of  its  length  from  one  of  its  ends  ought 
to  emit  the  same  note  as  the  half  rod  held  in  the  middle. 
When  both  notes  are  sounded  together  they  are  heard  to 
be  identical  in  pitch. 

Fig.  88,  a  and  &,  c  and  d,  e  and  /,  shows  the  three  first 
FIG.  88. 


divisions  of  a  rod  free  at  both  ends  and  vibrating  longi- 
tudinally. The  nodes,  as  before,  are  marked  by  transverse 
dots,  the  direction  of  the  pulses  being  shown  by  arrows. 
The  order  of  the  tones  is  that  of  the  numbers  1,  2,  3, 
4,  etc. 


EXAMINATION  BY  POLARIZED  LIGHT. 


197 


§  6.  Action  of  Sonorous  Vibrations  on  Polarized  Light. 

When  a  tube  or  rod  vibrating  longitudinally  yields  its 
fundamental  tone,  its  two  ends  are  in  a  state  of  free  vibra- 
tion, the  glass  there  suffering  neither  strain  nor  pressure. 
The  case  at  the  centre  is  exactly  the  reverse;  here  there 
is  no  vibration,  but  a  quick  alternation  of  tension  and 
compression.  When  the  sonorous  pulses  meet  at  the  centre 
they  squeeze  the  glass;  when  they  recoil  they  strain  it. 
Thus  while  at  the  ends  we  have  the  maximum  of  vibration, 
but  no  change  of  density,  at  the  centre  we  have  the  maxi- 
mum changes  of  density,  but  no  vibration. 

We  have  now  cleared  the  way  for  the  introduction  of  a 
very  beautiful  experiment  made  many  years  ago  by  Biot, 
but  never,  to  my  knowledge,  repeated  on  the  scale  here 
presented  to  you.  The  beam  from  our  electric  lamp,  L, 
Fig.  89,  being  sent  through  a  prism,  B,  of  bi-refracting 

FIG.  89. 


-- 


spar,  a  beam  of  polarized  light  is  obtained.  This  beam 
impinges  on  a  second  prism  of  spar,  n,  but,  though  both 
prisms  are  perfectly  transparent,  the  light  which  has 


198  SOUND. 

passed  through  the  first  cannot  get  through  the  second. 
By  introducing  a  piece  of  glass  between  the  two  prisms, 
and  subjecting  the  glass  to  either  strain  or  pressure,  the 
light  is  enabled  to  pass  through  the  entire  system. 

I  now  introduce  between  the  prisms  B  and  n  a  rec- 
tangle, s  s',  of  plate  glass,  6  feet  long,  2  inches  wide,  and 
^  of  an  inch  thick,  which  is  to  be  thrown  into  longitudinal 
vibration.  The  beam  from  L  passes  through  the  glass  at 
a  point  near  its  centre,  which  is  held  in  a  vice,  c,  so  that 
when  a  wet  cloth  is  passed  over  one  of  the  halves,  c  s',  of 
the  strip,  the  centre  will  be  a  node.  During  its  longitu- 
dinal vibration  the  glass  near  the  centre  is,  as  already 
explained,  alternately  strained  and  compressed;  and  this 
successive  strain  and  pressure  so  changes  the  condition 
of  the  light  as  to  enable  it  to  pass  through  the  second 
prism.  The  screen  is  now  dark;  but  on  passing  the 
wetted  cloth  briskly  over  the  glass  a  brilliant  disk  of  light, 
three  feet  in  diameter,  flashes  out  upon  the  screen.  The 
vibration  quickly  subsides,  and  the  luminous  disk  as  quick- 
ly disappears,  to  be,  however,  revived  at  will  by  the  pas- 
sage of  the  wetted  cloth  along  the  glass. 

The  light  of  this  disk  appears  to  be  continuous,  but  it 
is  really  intermittent,  for  it  is  only  when  the  glass  is  under 
strain  or  pressure  that  the  light  can  get  through.  In 
passing  from  strain  to  pressure,  and  from  pressure  to 
strain,  the  glass  is  for  a  moment  in  its  natural  state,  which, 
if  it  continued,  would  leave  the  screen  dark.  But  the 
impressions  of  brightness,  due  to  the  strains  and  pressures, 
remain  far  longer  upon  the  retina  than  is  necessary  to 
abolish  the  intervals  of  darkness;  hence  the  screen  ap- 
pears illuminated  by  a  continuous  light.  When  the  glass 
rectangle  is  shifted  so  as  to  cause  the  beam  of  polarized 
light  to  pass  through  it  close  to  its  end,  s,  the  longitudinal 
vibrations  of  the  glass  have  no  effect  whatever  upon  the 
polarized  beam. 


VIBRATIONS  OF  WOODEN  RODS.  199 

Thus,  by  means  of  this  subtile  investigator,  we  demon- 
strate that,  while  the  centre  of  the  glass,  where  the  vibra- 
tion is  nil,  is  subjected  to  quick  alternations  of  strain  and 
pressure,  the  ends  of  the  rectangle,  where  the  vibration  is 
a  maximum,  suffer  neither.1 

§  7.  Vibrations  of  Rods  of  Wood:  Determination  of 
Relative  Velocities  in  Different  Woods. 

Rods  of  wood  and  metal  also  yield  musical  tones  when 
they  vibrate  longitudinally.  Here,  however,  the  rubber 
employed  is  not  a  wet  cloth,  but  a  piece  of  leather  covered 
with  powdered  resin.  The  resined  fingers  also  elicit  the 
music  of  the  rods.  The  modes  of  vibration  here  are  those 
already  indicated,  the  pitch,  however,  varying  with  the 
velocity  of  the  sonorous  pulse  in  the  respective  substances. 
When  two  rods  of  the  same  length,  the  one  of  deal,  the 
other  of  Spanish  mahogany,  are  sounded  together,  the 
pitch  of  the  one  is  much  lower  than  that  of  the  other. 
Why  ?  Simply  because  the  sonorous  pulses  pass  more  slow- 
ly through  the  mahogany  than  through  the  deal.  Can  we 
find  the  relative  velocity  of  sound  through  both?  With 
the  greatest  ease.  We  have  only  to  carefully  shorten  the 
mahogany  rod  till  it  yields  the  same  note  as  the  deal  one. 
The  notes,  rendered  approximate  by  the  first  trials,  are 
now  identical.  Through  this  rod  of  mahogany  4  feet  long, 
and  through  this  rod  of  deal  6  feet  long,  the  sound-pulse 
passes  in  the  same  time,  and  these  numbers  express  the 
relative  velocities  of  sound  through  the  two  substances. 

Modes  of  investigation,  which  could  only  be  hinted  at 
in  our  earlier  lectures,  are  now  falling  naturally  into  our 
hands.  When  in  the  first  lecture  the  velocity  of  sound 
in  air  was  spoken  of,  many  possible  methods  of  determin- 
ing this  velocity  must  have  occurred  to  your  minds,  be- 
cause here  we  have  miles  of  space  to  operate  upon.  Its 
1  This 'experiment  succeeds  almost  equally  well  with  a  glass  tube. 


200  SOUND. 

velocity  through  wood  or  metal,  where  such  distances  are 
out  of  the  question,  is  determined  in  the  simple  manner 
just  indicated.  From  the  notes  which  they  emit  when 
suitably  prepared,  we  may  infer  with  certainty  the  rela- 
tive velocities  of  sound  through  different  solid  substances; 
and  determining  the  ratio  of  the  velocity  in  any  one  of 
them  to  its  velocity  in  air,  we  are  able  to  draw  up  a  table 
of  absolute  velocities.  But  how  is  air  to  be  introduced 
into  the  series?  We  shall  soon  be  able  to  answer  this 
question,  approaching  it,  however,  through  a  number  of 
phenomena  with  which,  at  first  sight,  it  appears  to  have 
no  connection. 


RESONANCE. 

§  8.  Experiments  with  Resonant  Jars.     Analysis  and 
Explanation. 

The  series  of  tuning-forks  now  before  you  have  had 
their  rates  of  vibration  determined  by  the  siren.  One, 
you  will  remember,  vibrates  256  times  in  a  second,  the 
length  of  its  sonorous  wave  being  4  feet  4  inches.  It  is 
detached  from  its  case,  so  that  when  struck  against  a  pad 
you  hardly  hear  it.  When  held  over  this  glass  jar,  A  B, 
Fig.  90,  18  inches  deep,  you  still  fail  to  hear  the  sound  of 
the  fork.  Preserving  the  fork  in  its  position,  I  pour  water 
with  the  least  possible  noise  into  the  jar.  The  column  of 
air  underneath  the  fork  shortens,  the  sound  augments  in 
intensity,  and  when  the  water  has  reached  a  certain  level 
it  bursts  forth  with  extraordinary  power.  A  greater  quan- 
tity of  water  causes  the  sound  to  sink,  and  become  finally 
inaudible,  as  at  first.  By  pouring  the  water  carefully  out 
a  point  is  reached  where  the  reenforcement  of  the  sound 


CONDITIONS  OF  RESONANCE. 


201 


FIG  90. 


again  occurs.    Experimenting  thus,  we  learn  that  there  is 

one  particular  length 

of  the  column  of  air 

which,  when  the  fork 

is    placed    above     it, 

produces  a  maximum 

augmentation    of    the 

sound.  This  reenforce- 

ment  of  the  sound  is 

named  resonance. 

Operating  in  the 
same  way  with  all  the 
forks  in  succession,  a 
column  of  air  is  found 
for  each,  which  yields 
a  maximum  resonance. 
These  columns  become 
shorter  as  the  rapidity 
of  vibration  increases. 

In  Fig.  91  the  series  of  jars  is  represented,  the  number  of 
vibrations  to  which  each  re- 
sounds being  placed  above  it. 

What  is  the  physical 
meaning  of  this  very  won- 
derful effect?  To  solve  this 
question  we  must  revive  our 
knowledge  of  the  relation 
of  the  motion  of  the  fork 
itself  to  the  motion  of  the 
sonorous  wave  produced  by 
the  fork.  Supposing  a  prong 

of  this  fork,  which  executes  256  vibrations  in  a  second, 
to  vibrate  between  the  points  a  and  &,  Fig.  92,  in  its 
motion  from  a  to  &  the  fork  generates  half  a  sonorous 
wave,  and  as  the  length  of  the  whole  wave  emitted  by 


256 


FIG.  91. 


384 


512 


202 


SOUND. 


this  fork  is  4  feet  4  inches,  at  the  moment  the  prong 
reaches  6  the  foremost  point  of  the  sonorous  wave  will  be 
at  c,  2  feet  2  inches  distant  from  the  fork.  The  motion 
of  the  wave,  then,  is  vastly  greater  than  that  of  the  fork. 

FIG.  92. 
26  inches 


V 


FIG.  93. 


In  fact,  the  distance  a  &  is,  in  this  case,  not  more  than  one- 
twentieth  of  an  inch,  while  the  wave  has  passed  over  a 
distance  of  26  inches.  With  forks  of  lower  pitch  the 
difference  would  be  still  greater. 

Our  next  question  is,  what  is  the  length  of  the  column 
of  air  which  resounds  to  this  fork?  By  measurement  with 
a  two-foot  rule  it  is  found  to  be  13  inches.  But  the  length 
of  the  wave  emitted  by  the  fork  is  52  inches;  hence  the 
length  of  the  column  of  air  which 
resounds  to  the  fork  is  equal  to  one- 
fourth  of  the  length  of  the  sound- 
wave produced  by  the  fork.  This 
rule  is  general,  and  might  be  illus- 
trated by  any  other  of  the  forks  in- 
stead of  this  one. 

Let  the  prong,  vibrating  between 
the  limits  a  and  &,  be  placed  over  its 
resonant  jar,  A  B,Fig.  93.  In  the  time 
required  by  the  prong  to  move  from 
a  to  &,  the  condensation  it  produces 
runs  down  to  the  bottom  of  the  jar, 
is  there  reflected,  and,  as  the  distance  to  the  bottom  and 


ANALYSIS  AND  EXPLANATION.  203 

back  is  26  inches,  the  reflected  wave  will  reach  the  fork 
at  the  moment  when  it  is  on  the  point  of  returning  from 
b  to  a.  The  rarefaction  of  the  wave  is  produced  by  the 
retreat  of  the  prong  from  b  to  a.  This  rarefaction  will 
also  run  to  the  bottom  of  the  jar  and  back,  overtaking  the 
prong  just  as  it  reaches  the  limit,  a,  of  its  excursion.  It 
is  plain  from  this  analysis  that  the  vibrations  of  the  fork 
are  perfectly  synchronous  with  the  vibrations  of  the  aerial 
column  A  B;  and  in  virtue  of  this  synchronism  the  motion 
accumulates  in  the  jar,  spreads  abroad  in  the  room,  and 
produces  this  vast  augmentation  of  the  sound. 

When  we  substitute  for  the  air  in  one  of  these  jars  a 
gas  of  different  elasticity,  we  find  the  length  of  the  re- 
sounding column  to  be  different.  The  velocity  of  sound 
through  coal-gas  is  to  its  velocity  in  air  about  as  8:5. 
Hence,  to  synchronize  with  our  fork,  a  jar  filled  with  coal- 
gas  must  be  deeper  than  one  filled  with  air.  I  turn  this 
jar,  18  inches  long,  upside  down,  and  hold  close  to  its 
open  mouth  our  agitated  tuning-fork.  It  is  scarcely  audi- 
ble. The  jar,  with  air  in  it,  is  5  inches  too  deep  for  this 
fork.  Let  coal-gas  now  enter  the  jar.  As  it  ascends  the 
note  at  a  certain  point  swells  out,  proving  that  for  the 
more  elastic  gas  a  depth  of  18  inches  is  not  too  great.  In 
fact,  it  is  not  great  enough ;  for  if  too  much  gas  be  allowed 
to  enter  the  jar  the  resonance  is  weakened.  By  suddenly 
turning  the  jar  upright,  still  holding  the  fork  close  to  its 
mouth,  the  gas  escapes,  and  at  the  point  of  proper  admixt- 
ure of  gas  and  air  the  note  swells  out  again.1 

§  9.  Reenforcement  of  Bell  by  Resonance. 

This  fine,  sonorous  bell,  Fig,  94,  is  thrown  into  intense 
vibration  by  the  passage  of  a  resined  bow  across  its  edge. 
You  hear  its  sound,  pure,  but  not  very  forcible.  When, 

1  This  experiment  is  more  easily  executed  with  hydrogen  than  with 
coal-gas. 


204  SOUND. 

however,  the  open  mouth  of  this  large  tube,  which  is 
closed  at  one  end,  is  brought  close  to  one  of  the  vibrating 
segments  of  the  bell,  the  tone  swells  into  a  musical  roar. 


FIG.  94. 


As  the  tube  is  alternately  withdrawn  and  advanced,  the 
sound  sinks  and  swells  in  this  extraordinary  manner. 

The  second  tube,  open  at  both  ends,  is  capable  of  being 
lengthened  and  shortened  by  a  telescopic  slider.  When 
brought  near  the  vibrating  bell,  the  resonance  is  feeble. 
On  lengthening  the  tube  by  drawing  out  the  slider  at  a 
certain  point,  the  tone  swells  out  as  before.  If  the  tube 
be  made  longer,  the  resonance  is  again  enfeebled.  Note 
the  fact,  which  shall  be  explained  presently,  that  the  open 
tube  which  gives  the  maximum  resonance  is  exactly  twice 
the  length  of  the  closed  one.  For  these  fine  experiments 
we  are  indebted  to  Savart. 

§  10.  Expenditure  of  Motion  in  Resonance. 

With  the  India-rubber  tube  employed  in  our  third 
chapter  it  was  found  necessary  to  time  the  impulses  prop- 
erly, so  as  to  produce  the  various  ventral  segments.  I 
could  then  feel  that  the  muscular  work  performed,  when 
the  impulses  were  properly  timed,  was  greater  than  when 


EXPENDITURE  OP  MOTION  IN  RESONANCE.       205 

they  were  irregular.  The  same  truth  may  be  illustrated 
by  a  claret-glass  half  filled  with  water.  Endeavor  to 
move  your  hand  to  and  fro,  in  accordance  with  the  oscil- 
lating period  of  the  water:  when  you  have  thoroughly 
established  synchronism,  the  work  thrown  upon  the  hand 
apparently  augments  the  weight  of  the  water.  So  like- 
wise with  our  tuning-fork;  when  its  impulses  are  timed 
to  the  vibrations  of  the  column  of  air  contained  in  this 
jar,  its  work  is  greater  than  when  they  are  not  so  timed. 
As  a  consequence  of  this  the  tuning-fork  comes  sooner  to 
rest  when  it  is  placed  over  the  jar  than  when  it  is  permit- 
ted to  vibrate  either  in  free  air,  or  over  a  jar  of  a  depth 
unsuited  to  its  periods  of  vibration.1 

Reflecting  on  what  we  have  now  learned,  you  would 
have  little  difficulty  in  solving  the  following  beautiful 
problem:  You  are  provided  with  a  tuning-fork  and  a 
siren,  and  are  required  by  means  of  these  two  instruments 
to  determine  the  velocity  of  sound  in  air.  To  solve  this 
problem  you  lack,  if  anything,  the  mere  power  of  manip- 
ulation which  practice  imparts.  You  would  first  deter- 
mine, by  means  of  the  siren,  the  number  of  vibrations 
executed  by  the  tuning-fork  in  a  second;  you  would  then 
determine  the  length  of  the  column  of  air  which  resounds 
to  the  fork.  This  length  multiplied  by  4  would  give  you, 
approximately,  the  wave-length  of  the  fork,  and  the  wave- 
length multiplied  by  the  number  of  vibrations  in  a  second 
would  give  you  the  velocity  in  a  second.  Without  quit- 
ting your  private  room,  therefore,  you  could  solve  this 
important  problem.  We  will  go  on,  if  you  please,  in  this 
fashion,  making  our  footing  sure  as  we  advance. 

1  Only  an  extremely  small  fraction  of  the  fork's  motion  is,  however, 
converted  into  sound.  The  remainder  is  expended  in  overcoming  the 
internal  friction  of  its  own  particles.  In  other  words,  nearly  the  whole 
of  the  motion  is  converted  into  heat. 


206  SOUND. 

§  11.  Resonators  of  Helmholtz. 

Helmholtz  has  availed  himself  of  the  principle  of  reso- 
nance in  analyzing  composite  sounds.  He  employs  little 
hollow  spheres,  called  resonators,  one  of  which  is  shown 
in  Fig.  94a.  The  small  projection  6,  which  has  an  orifice, 

FIG.  94a. 


is  placed  in  the  ear,  while  the  sound-waves  enter  the  hol- 
low sphere  through  the  wide  aperture  at  a.  Reenforced 
by  the  resonance  of  such  a  cavity,  and  rendered  thereby 
more  powerful  than  its  companions,  a  particular  note  of  a 
composite  clang  may  be  in  a  measure  isolated  and  studied 
alone. 


ORGAN-PIPES. 

§  12.  Principles  of  Resonance  applied  to  Organ-Pipes. 

Thus  disciplined  we  are  prepared  to  consider  the  sub- 
ject of  organ-pipes,  which  is  one  of  great  importance. 
Before  me  on  the  table  are  two  resonant  jars,  and  in  my 
right  hand  and  my  left  are  held  two  tuning-forks.  I  agi- 
tate both,  and  hold  them  over  this  jar.  One  of  them  only 
is  heard.  Held  over  the  other  jar,  the  other  fork  alone 
is  heard.  Each  jar  selects  that  fork  whose  periods  of 


VIBRATING  COLUMNS  OF  AIR. 


207 


FIG.  95. 


vibration  synchronize  with  its  own.  And  instead  of  two 
forks  suppose  several  of  them  to  be  held  over  the  jar; 
from  the  confused  assemblage  of  pulses  thus  generated, 
the  jar  would  select  and  reenforce  that  one  which  corre- 
sponds to  its  own  period  of  vibration. 

When  I  blow  across  the  open  mouth  of  the  jar;  or, 
better  still,  for  the  jar  is  too  wide  for  this  experiment,  when 
I  blow  across  the  open  end  of  a  glass  tube,  t  u,  Fig.  95,  of 
the  same  length  as  the  jar,  a  fluttering  of  the  air  is  thereby 
produced,  an  assemblage  of  pulses  at  the  open  mouth  of  the 
tube  being  generated.  And  what  is  the  con- 
sequence? The  tube  selects  that  pulse  of  the 
flutter  which  is  in  synchronism  with  itself 
and  raises  it  to  a  musical  sound.  The  sound, 
you  perceive,  is  precisely  that  obtained  when 
the  proper  tuning-fork  is  placed  over  the  tube. 
The  column  of  air  within  the  tube  has,  in 
this  case,  virtually  created  its  own  tuning- 
fork;  for  by  the  reaction  of  its  pulses  upon 
the  sheet  of  air  issuing  from  the  lips  it  has 
compelled  that  sheet  to  vibrate  in  synchron- 
ism with  itself,  and  made  it  thus  act  the  part 
of  the  tuning-fork. 

Selecting  for  each  of  the  other  tuning- 
forks  a  resonant  tube,  in  every  case,  on  blow- 
ing across  the  open  end  of  the  tube,  a  tone  is 
produced  identical  in  pitch  with  that  obtained  through 
resonance. 

When  different  tubes  are  compared,  the  rate  of  vibra- 
tion is  found  to  be  inversely  proportional  to  the  length  of 
the  tube.  These  three  tubes  are  24,  12,  and  6  inches  long, 
respectively.  I  blow  gently  across  the  24-inch  tube,  and 
bring  out  its  fundamental  note;  similarly  treated,  the  12- 
inch  tube  yields  the  octave  of  the  note  of  the  24-inch.  In 
like  manner  the  6-inch  tube  yields  the  octave  of  the  12- 
14 


208  SOUND. 

inch.  It  is  plain  that  this  must  be  the  case;  for,  the  rate 
of  vibration  depending  on  the  distance  which  the  pulse 
has  to  travel  to  complete  a  vibration,  if  in  one  case  this 
distance  be  twice  what  it  is  in  another,  the  rate  of  vibra- 
tion must  be  twice  as  slow.  In  general  terms,  the  rate  of 
vibration  is  inversely  proportional  to  the  length  of  the 
tube  through  which  the  pulse  passes. 

§  13.   Vibrations  of  Stopped  Pipes:  Modes  of  Division: 
Overtones. 

But  that  the  current  of  air  should  be  thus  able  to  ac- 
commodate itself  to  the  requirements  of  the  tube,  it  must 
enjoy  a  certain  amount  of  flexibility.  A  little  reflection 
will  show  you  that  the  power  of  the  reflected  pulse  over 
the  current  must  depend  to  some  extent  on  the  force  of 
the  current.  A  stronger  current,  like  a  more  powerfully 
stretched  string,  requires  a  great  force  to  deflect  it,  and 
when  deflected  vibrates  more  quickly.  Accordingly,  to 
obtain  the  fundamental  note  of  this  24-inch  tube,  we  must 
blow  very  gently  across  its  open  end ;  a  rich,  full,  and  for- 
cible musical  tone  is  then  produced.  "With  a  little  stronger 
blast  the  sound  approaches  a  mere  rustle ;  blowing  stronger 
still,  a  tone  is  obtained  of  much  higher  pitch  than  the 
fundamental  one.  This  is  the  first  overtone  of  the  tube, 
to  produce  which  the  column  of  air  within  it  has  divided 
itself  into  two  vibrating  parts,  with  a  node  between  them. 
With  a  still  stronger  blast  a  still  higher  note  is  obtained. 
The  tube  is  now  divided  into  three  vibrating  parts,  sepa- 
rated from  each  other  by  two  nodes.  Once  more  I  blow 
with  sudden  strength;  a  higher  note  than  any  before  ob- 
tained is  the  consequence. 

In  Fig.  96  are  represented  the  divisions  of  the  column 
of  air  corresponding  to  the  first  three  notes  of  a  tube 
stopped  at  one  end.  At  a  and  &,  which  correspond  to  the 
fundamental  note,  the  column  is  undivided ;  the  bottom  of 


STOPPED  PIPES. 


209 


FIG.  96. 


the  tube  is  the  only  node,  and  the  pulse  simply  moves  up 
and  down  from  top  to  bottom,  as  denoted  by  the  arrows. 
In  c  and  dy  which  correspond  to  the  first  overtone  of  the 
tube,  we  have  one  nodal  surface  shown  by  dots  at  x, 
against  which  the  pulses  abut,  and  from  which  they  are 
reflected  as  from  a  fixed  surface.  This  nodal  surface  is 
situated  at  one-third  of 
the  length  of  the  tube 
from  its  open  end.  In 
e  and  /,  which  correspond 
to  the  second  overtone, 
we  have  two  nodal  sur- 
faces, the  upper  one,  x', 
of  which  is  at  one-fifth  of 
the  length  of  the  tube 
from  its  open  end,  the 

remaining  four-fifths  being  divided  into  two  equal  parts 
by  the  second  nodal  surface.  The  arrows,  as  before,  mark 
the  direction  of  the  pulses. 

We  have  now  to  inquire  into  the  relation  of  these 
successive  notes  to  each  other.  The  space  from  node  to 
node  has  been  called  all  through  "  a  ventral  segment;  " 
hence  the  space  between  the  middle  of  a  ventral  segment 
and  a  node  is  a  semi-ventral  segment.  You  will  readily 
bear  in  mind  the  law  that  the  number  of  vibrations 
is  directly  proportional  to  the  number  of  semi-ventral 
segments  into  which  the  column  of  air  within  the  tube  is 
divided.  Thus,  when  the  fundamental  note  is  sounded,  we 
have  but  a  single  semi-ventral  segment,  as  at  a  and  &.  The 
bottom  here  is  a  node,  and  the  open  end  of  the  tube,  where 
the  air  is  agitated,  is  the  middle  of  a  ventral  segment. 
The  mode  of  division  represented  in  c  and  d  yield  three 
semi-ventral  segments;  in  e  and  f  we  have  five.  The  vi- 
brations, therefore,  corresponding  to  this  series  of  notes, 
augment  in  the  proportion  of  the  series  of  odd  numbers, 


210  SOUND. 

1:3:5.  And  could  we  obtain  still  higher  notes,  their 
relative  rates  of  vibration  would  continue  to  be  represented 
by  the  odd  numbers,  7,  9,  11,  13,  etc.,  etc. 

It  is  evident  that  this  must  be  the  law  of  succession. 
For  the  time  of  vibration  in  c  or  d  is  that  of  a  stopped 
tube  of  the  length  x  y;  but  this  length  is  one-third  of  the 
length  of  the  whole  tube,  consequently  its  vibrations  must 
be  three  times  as  rapid.  The  time  of  vibration  in  e  or  /  is 
that  of  a  stopped  tube  of  the  length  x'  y',  and  inasmuch  as 
this  length  is  one-fifth  that  of  the  whole  tube,  its  vibra- 
tions must  be  five  times  as  rapid.  We  thus  obtain  the 
succession  1,  3,  5,  and  if  we  pushed  matters  further 
we  should  obtain  the  continuation  of  the  series  of  odd 
numbers. 

And  here  it  is  once  more  in  your  power  to  subject  my 
statements  to  an  experimental  test.  Here  are  two  tubes, 
one  of  which  is  three  times  the  length  of  the  other.  I 
sound  the  fundamental  note  of  the  longest  tube,  and  then 
the  next  note  above  the  fundamental.  The  vibrations  of 
these  two  notes  are  stated  to  be  in  the  ratio  of  1 :  3.  This 
latter  note,  therefore,  ought  to  be  of  precisely  the  same 
pitch  as  the  fundamental  note  of  the  shorter  of  the  two 
tubes.  When  both  tubes  are  sounded  their  notes  are 
identical. 

It  is  only  necessary  to  place  a  series  of  such  tubes  of 
different  lengths  thus  together  to  form  that  ancient  instru- 
ment, Pan's  pipes,  p  p',  Fig.  97  (next  page),  with  which 
we  are  so  well  acquainted. 

The  successive  divisions,  and  the  relation  of  the  over- 
tones of  a  rod  fixed  at  one  end  (described  in  p.  193),  are 
plainly  identical  with  those  of  a  column  of  air  in  a  tube 
stopped  at  one  end,  which  we  have  been  here  considering. 


OPEN  PIPES.  211 

§  14.   Vibrations  of  Open  Pipes:  Modes  of  Division: 
Overtones. 

From  tubes  closed  at  one  end,  and  which,  for  the  sake 
of  brevity,  may  be  called  stopped  tubes,  we  now  pass  to 
tubes  open  at  both  ends,  which  we  shall  call  open  tubes. 
Comparing,  in  the  first  instance,  a  stopped  tube  with  an 
open  one  of  the  same  length,  we  find  the  note  of  the  latter 
an  octave  higher  than  that  of  the  former.  This  result  is 
general.  To  make  an  open  tube  yield  the  same  note  as  a 
closed  one,  it  must  be  twice  the  length  of  the  latter.  And, 
since  the  length  of  a  closed  tube  sounding  its  fundamental 
note  is  one-fourth  of  the  pIQ  ^ 

length  of  its  sonorous  wave, 
the  length  of  an  open  tube 
is  one-half  that  of  the  sono- 
rous wave  that  it  produces. 

It  is  not  easy  to  obtain 
a  sustained  musical  note  by 
blowing  across  the  end  of 
an  open  glass  tube;  but  a 
mere  puff  of  breath  across  the  end  reveals  the  pitch  to  the 
disciplined  ear.  In  each  case  it  is  that  of  a  closed  tube 
half  the  length  of  the  open  one. 

There  are  various  ways  of  agitating  the  air  at  the  ends 
of  pipes  and  tubes,  so  as  to  throw  the  air-columns  within 
them  into  vibration.  In  organ-pipes  this  is  done  by  blow- 
ing a  thin  sheet  of  air  against  a  sharp  edge.  You  will 
have  no  difficulty  in  understanding  the  construction  of  an 
open  organ-pipe,  from  this  model,  Fig.  98,  one  side  of 
which  has  been  removed  so  that  you  may  see  its  inner 
parts.  Through  the  tube  t  the  air  passes  from  the  wind- 
chest  into  the  chamber,  c,  which  is  closed  at  the  top,  save  a 
narrow  slit,  e  d,  through  which  the  compressed  air  of  the 
chamber  issues.  This  thin  air-current  breaks  against  the 


212 


SOUND. 


FIG.  98.  sharp  edge,  a  &,  and  there  pro- 
duces a  fluttering  noise,  and  the 
proper  pulse  of  this  flutter  is 
converted  by  the  resonance  of 
the  pipe  above  into  a  musical 
sound.  The  open  space  be- 
tween the  edge,  a  &,  and  the  slit 
below  it  is  called  the  embou- 
chure. Fig.  99  represents  a 
stopped  pipe  of  the  same  length 
as  that  shown  in  Fig.  98,  and 
hence  producing  a  note  an  oc- 
tave lower. 

Instead  of  a  fluttering  sheet 
of  air,  a  tuning-fork  whose  rate 
of  vibration  synchronizes  with 
that  of  the  organ-pipe  may  be 
placed  at  the  embouchure,  as  at 
A  B,  Fig.  100.  The  pipe  will 
resound.  Here,  for  example, 
are  four  open  pipes  of  different 
lengths,  and  four  tuning-forks 
of  different  rates  of  vibration. 
Striking  the  most  slowly  vi- 
brating fork,  and  bringing  it 
near  the  embouchure  of  the 
longest  pipe,  the  pipe  speaks 
powerfully.  When  blown  into, 
the  same  pipe  yields  a  tone 
identical  with  that  of  the  tun- 
ing-fork. Going  through  all 
the  pipes  in  succession,  we  find 
in  each  case  that  the  note  ob- 
tained by  blowing  into  the  pipe 
is  exactly  that  produced  when 


FIG.  99. 


RESONANCE  APPLIED  TO  ORGAN-PIPES. 


213 


the  proper  tuning-fork  is  placed  at  the  embouchure.  Con- 
ceive now  the  four  forks  placed  together  near  the  same 
embouchure;  we  should  have  pulses  of  four  different 
periods  there  excited;  but  out  of  the  four  the  pipe  would 
select  only  one.  And  if  four  hundred  vibrating  forks 
could  be  placed  there  instead  of  four,  the  pipe  would  still 
make  the  proper  selection.  This  it  also  does  when  for 
the  pulses  of  tuning-forks  we  substitute  the  assemblage  of 
pulses  created  by  the  current 
of  air  when  it  strikes  against 
the  sharp  upper  edge  of  the 
embouchure. 

The  heavy  vibrating  mass 
of  the  tuning-fork  is  prac- 
tically uninfluenced  by  the 
motion  of  the  air  within 
the  pipe.  But  this  is  not 
the  case  when  air  itself  is 
the  vibrating  body.  Here,  as 
before  explained,  the  pipe 
creates,  as  it  were,  its  own 
tuning-fork,  by  compelling 
the  fluttering  stream  at  its 
embouchure  to  vibrate  in 
periods  answering  to  its  own. 

The  condition  of  the  air  within  an  open  organ-pipe, 
when  its  fundamental  note  is  sounded,  is  that  of  a  rod 
free  at  both  ends,  held  at  its  centre,  and  caused  to  vibrate 
longitudinally.  The  two  ends  are  places  of  vibration,  the 
centre  is  a  node.  Is  there  any  way  of  feeling  the  vibrat- 
ing air-column  so  as  to  determine  its  nodes  and  its 
places  of  vibration?  The  late  excellent  William  Hopkins 
has  taught  us  the  following  mode  of  solving  this  problem : 
Over  a  little  hoop  is  stretched  a  thin  membrane,  forming 
a  little  tambourine.  The  front  of  this  organ-pipe,  p  p', 


214 


SOUND. 


PIG  101 


Fig.  101,  is  of  glass,  through  which  you  can  see  the  posi- 
tion of  any  body  within  it.  By  means  of  a  string,  the  little 
tambourine,  w,  can  be  raised  or  lowered  at  pleasure 
througK  the  entire  length  of  the  pipe.  When  held  above 
the  upper  end  of  the  pipe,  you  hear  the  loud  buzzing  of 
the  membrane.  When  lowered  into  the  pipe,  it  continues 
to  buzz  for  a  time;  the  sound  becoming  gradually  feebler, 
anc^  nna%  ceasing  totally.  It  is  now  in 
the  middle  of  the  pipe,  where  it  cannot 
vibrate,  because  the  air  around  it  is  at 
rest.  On  lowering  it  still  further,  the 
buzzing  sound  instantly  recommences,  and 
continues  down  to  the  bottom  of  the 
pipe.  Thus,  as  the  membrane  is  raised 
and  lowered  in  quick  succession,  during 
every  descent  and  ascent,  we  have  two 
periods  of  sound  separated  from  each 
other  by  one  of  silence.  If  sand  were 
strewed  upon  the  membrane,  it  would 
dance  above  and  below,  but  it  would  be 
quiescent  at  the  centre.  We  thus  prove 
experimentally  that,  when  an  organ-pipe 
sounds  its  fundamental  note,  it  divides  it- 
self into  two  semi-ventral  segments  sepa- 
rated by  a  node. 

What  is  the  condition  of  the  air  at 
this  node?  Again,  that  of  the  middle  of 
a  rod,  free  at  both  ends,  and  yielding  the 
fundamental  note  of  its  longitudinal  vi- 
bration. The  pulses  reflected  from  both 
ends  of  the  rod,  or  of  the  column  of  air, 
meet  in  the  middle,  and  produce  compression;  they  then 
retreat  and  produce  rarefaction.  Thus,  while  there  is  no 
vibration  in  the  centre  of  an  organ-pipe,  the  air  there  under- 
goes the  greatest  changes  of  density.  At  the  two  ends  of 


NODES  OF  ORGAN-PIPES.  215 

the  pipe,  on  the  other  hand,  the  air-particles  merely  swing 
up  and  down  without  sensible  compression  or  rarefaction. 
If  the  sounding  pipe  were  pierced  at  the  centre,  and 
the  orifice  stopped  by  a  membrane,  the  air,  when  condensed, 
would  press  the  membrane  outward,  and,  when  rarefied, 
the  external  air  would  press  the  membrane  inward.  The 
membrane  would  therefore  vibrate  in  unison  with  the 
column  of  air.  The  organ-pipe,  Fig.  102,  is  so  arranged 
that  a  small  jet  of  gas,  6,  can  be  lighted  opposite  the  centre 
of  the  pipe,  and  there  acted  upon  by  the  vibrations  of  a 
membrane.  Two  other  gas-jets,  a  and  c,  are  placed  nearly 
midway  between  the  centre  and  the  two  ends  of  the  pipe. 
The  three  burners,  a,lt,cy  are  fed  in  the  following  manner: 


through  the  tube,  t,  the  gas  enters  the  hollow  chamber, 
e  d,  from  which  issue  three  little  bent  tubes,  shown  in  the 
figure,  each  communicating  with  a  capsule  closed  under- 
neath by  the  membrane.  This  is  in  direct  contact  with 
the  air  of  the  organ-pipe.  From  the  three  capsules  issue 
the  three  little  burners,  with  their  flames,  a,  b,  c. 

Blowing  into  the  pipe  so  as  to  sound  its  fundamental 
note,  the  three  flames  are  agitated,  but  the  central  one 
is  most  so.  Lowering  the  flames  so  as  to  render  them 
very  small,  and  blowing  again,  the  central  flame,  &,  is  ex- 
tinguished, while  the  others  remain  lighted.  The  experi- 
ment may  be  performed  half  a  dozen  times  in  succession; 
the  sounding  of  the  fundamental  note  always  quenches  the 
middle  flame. 


216  SOUND. 

By  blowing  more  sharply  into  the  pipe,  it  is  caused 
to  yield  its  first  overtone.  The  middle  node  no  longer 
exists.  The  centre  of  the  pipe  is  now  a  place  of  maximum 
vibration,  while  two  nodes  are  formed  midway  between 
the  centre  and  the  two  ends.  But  if  this  be  the  case,  and 
if  the  flame  opposite  the  node  be  always  blown  out,  then, 
when  the  first  overtone  of  this  pipe  is  sounded,  the  two 
flames  a  and  c  ought  to  be  extinguished,  while  the  central 
flame  remains  lighted.  This  is  the  case.  When  the  first 
harmonic  is  sounded  the  two  nodal  flames  are  infallibly  ex- 
tinguished, while  the  flame  b  in  the  middle  of  the  ventral 
segment  is  not  sensibly  disturbed. 

There  is  no  theoretic  limit  to  the  subdivision  of  an 
organ-pipe,  either  stopped  or  open.  In  stopped  pipes  we 
begin  with  1  semi-ventral  segment,  and  pass  on  to  3,  5,  7, 
etc.,  semi-ventral  segments,  the  number  of  vibrations  of 
the  successive  notes  augmenting  in  the  same  ratio.  In 
open  pipes  we  begin  with  2  semi-ventral  segments,  and 
pass  on  to  4,  6,  8,  10,  etc.,  the  number  of  vibrations  of 
the  successive  notes  augmenting  in  the  same  ratio;  that 
is  to  say,  in  the  ratio  1:2:3:4:5,  etc.  When,  therefore, 
we  pass  from  the  fundamental  tone  to  the  first  overtone 
in  an  open  pipe,  we  obtain  the  octave  of  the  fundamental. 
When  we  make  the  same  passage  in  a  stopped  pipe,  we 
obtain  a  note  a  fifth  above  the  octave.  No  intermediate 
modes  of  vibration  are  in  either  case  possible.  If  the 
fundamental  tone  of  a  stopped  pipe  be  produced  by  100 
vibrations  a  second,  the  first  overtone  will  be  produced 
by  300  vibrations,  the  second  by  500,  and  so  on.  Such 
a  pipe,  for  example,  cannot  execute  200  or  400  vibrations 
in  a  second.  In  like  manner  the  open  pipe,  whose  funda- 
mental note  is  produced  by  100  vibrations  a  second,  cannot 
vibrate  150  times  in  a  second,  but  passes,  at  a  jump,  to 
200,  300,  400,  and  so  on. 

In  open  pipes,  as  in  stopped  ones,  the  number  of  vibra- 


DIVISIONS  OF  OPEN  PIPE. 


217 


tions  executed  in  the  unit  of  time  is  inversely  proportional 
to  the  length  of  the  pipe.  This  follows  from  the  fact, 
already  dwelt  upon  so  often,  that  the  time  of  a  vibration  is 
determined  by  the  distance  which  the  sonorous  pulse  has 
to  travel  to  complete  a  vibration. 

In  Fig.  103,  a  and  6  (at  the  bottom)  represent  the 
division  of  an  open  pipe  corresponding  to  its  fundamental 
tone;  c  and  d  represent  the  division  corresponding  to  its 
first,  e  and  /  the  di-  FIG.  103. 

vision  corresponding 
to  its  second  over- 
tone, the  dots  mark- 
ing the  nodes.  The 
distance  m  n  is  one- 
half,  o  p  is  one-fourth, 
and  s  t  is  one-sixth 
of  the  whole  length 
of  the  pipe.  But  the 
pitch  of  a  is  that  of 
a  stopped  pipe  equal 
in  length  to  m  n; 
the  pitch  of  c  is  that 
of  a  stopped  pipe  of 
the  length  op;  while 
the  pitch  of  e  is  that  of  a  stopped  pipe  of  the  length  s  t. 
Hence,  as  these  lengths  are  in  the  ratio  of  £:£:'•&,  or  as 
1 :  | :  ^,  the  rates  of  vibration  must  be  as  the  reciprocals 
of  these,  or  as  3  :  2  :  1.  From  the  mere  inspection,  there- 
fore, of  the  respective  modes  of  vibration,  we  can  draw  the 
inference  that  the  succession  of  tones  of  an  open  pipe  must 
correspond  to  the  series  of  natural  numbers. 

The  pipe  a,  Fig.  103,  has  been  purposely  drawn  twice 
the  length  of  a,  Fig.  93  (p.  202).  It  is  perfectly  mani- 
fest that  to  complete  a  vibration  the  pulse  has  to  pass 
over  the  same  distance  in  both  pipes,  and  hence  that  the 


n      p 

I 

1 

p    e 

a 

I 

\ 

0 

o 

f 

m 

t 

1 

I 

1 

\ 

t 

i 

i 

| 

I 

i 

i 

1 

a, 

b 

C 

d 

e 

/ 

218  SOUND. 

pitch  of  the  two  pipes  must  be  the  same.  The  open  pipe, 
a  n,  consists  virtually  of  two  stopped  ones,  with  the  cen- 
tral nodal  surface  at  m  as  their  common  base.  This  shows 
the  relation  of  a  stopped  pipe  to  an  open  one  to  be  that 
which  experiment  establishes. 

§  15.   Velocity  of  Sound  in  Gases,  Liquids,  and  Solids, 
determined  by  Musical  Vibrations. 

We  have  already  learned  that  the  relative  velocities  of 
sound  in  different  solid  bodies  may  be  determined  from 
the  notes  which  they  emit  when  thrown  into  longitu- 
dinal vibration.  It  was  remarked  at  the  time  that  to 
draw  up  a  table  of  absolute  velocities  we  only  required 
the  accurate  comparison  of  the  velocity  in  any  one  of 
those  solids  with  the  velocity  in  air.  We  are  now  in  a 
condition  to  supply  this  comparison.  For  we  have  learned 
that  the  vibrations  of  the  air  in  an  organ-pipe  open  at 
both  ends  are  executed  precisely  as  those  of  a  rod  free  at 
both  ends.  Any  difference  of  rapidity,  therefore,  between 
the  vibrations  of  a  rod  and  of  an  open  organ-pipe  of  the 
same  length  must  be  due  solely  to  the  different  velocities 
with  which  the  sonorous  pulses  are  propagated  through 
them.  Take  therefore  an  organ-pipe  of  a  certain  length, 
emitting  a  note  of  a  certain  pitch,  and  find  the  length  of 
a  rod  of  pine  which  yields  the  same  note.  This  length 
would  be  ten  times  that  of  the  organ-pipe,  which  would 
prove  the  velocity  of  sound  in  pine  to  be  ten  times  its 
velocity  in  air.  But  the  absolute  velocity  in  air  is  1,090 
feet  a  second;  hence  the  absolute  velocity  in  pine  is 
10,900  feet  a  second,  which  is  that  given  in  our  first 
chapter  (p.  TO).  To  the  celebrated  Chladni  we  are  in- 
debted for  this  beautiful  mode  of  determining  the  velocity 
of  sound  in  solid  bodies. 

We  had  also  in  our  first  lecture  a  table  of  the  velocities 
of  sound  in  other  gases  than  air.  I  am  persuaded  that 


VELOCITY   OF  SOUND.  219 

you  could  tell  me,  after  due  reflection,  how  this  table  was 
constructed.  It  would  only  be  necessary  to  find  a  series 
of  organ-pipes  which,  when  filled  with  the  different  gases, 
yield  the  same  note;  the  lengths  of  these  pipes  would 
give  the  relative  velocities  of  sound  through  the  gases. 
Thus  we  should  find  the  length  of  a  pipe  filled  with 
hydrogen  to  be  four  times  that  of  a  pipe  filled  with  oxy- 
gen, yielding  the  same  note,  and  this  would  prove  the 
velocity  of  sound  in  the  former  to  be  four  times  its 
velocity  in  the  latter. 

But  we  had  also  a  table  of  velocities  through  various 
liquids.  How  was  it  constructed?  By  forcing  the  liquids 
through  properly  constructed  organ-pipes,  and  comparing 
their  musical  tones.  Thus,  in  water  it  requires  a  pipe  a 
little  better  than  four  feet  long  to  produce  the  note  of  an 
air-pipe  one  foot  long;  and  this  proves  the  velocity  of 
sound  in  water  to  be  somewhat  more  than  four  times  its 
velocity  in  air.  My  object  here  is  to  give  you  a  clear 
notion  of  the  way  in  which  scientific  knowledge  enables 
us  to  cope  with  these  apparently  insurmountable  problems. 
It  is  not  necessary  to  go  into  the  niceties  of  these  measure- 
ments. You  will,  however,  readily  comprehend  that  all 
the  experiments  with  gases  might  be  made  with  the  same 
organ-pipe,  the  velocity  of  sound  in  each  respective  gas 
being  immediately  deduced  from  the  pitch  of  its  note. 
With  a  pipe  of  constant  length  the  pitch,  or,  in  other 
words,  the  number  of  vibrations,  would  be  directly  pro- 
portional to  the  velocity.  Thus,  comparing  oxygen  with 
hydrogen,  we  should  find  the  note  of  the  latter  to  be  the 
double  octave  of  that  of  the  former,  whence  we  should 
infer  the  velocity  of  sound  in  hydrogen  to  be  four  times 
its  velocity  in  oxygen.  The  same  remark  applies  to  ex- 
periments with  liquids.  Here  also  the  same  pipe  may  be 
employed  throughout,  the  velocities  being  inferred  from 
the  notes  produced  by  the  respective  liquids. 


220  SOUND. 

In  fact,  the  length  of  an  open  pipe  being,  as  already 
explained,  one-half  the  length  of  its  sonorous  wave,  it  is 
only  necessary  to  determine,  by  means  of  the  siren,  the 
number  of  vibrations  executed  by  the  pipe  in  a  second, 
and  to  multiply  this  number  by  twice  the  length  of  the 
pipe,  in  order  to  obtain  the  velocity  of  sound  in  the  gas  or 
liquid  within  the  pipe.  Thus,  an  open  pipe  26  inches 
long  and  filled  with  air  executes  256  vibrations  in  a  sec- 
ond. The  length  of  its  sonorous  wave  is  twice  26  inches, 
or  44  feet:  multiplying  256  by  4^  we  obtain  1,120  feet 
per  second  as  the  velocity  of  sound  through  air  of  this 
temperature.  Were  the  tube  filled  with  carbonic-acid  gas, 
its  vibrations  would  be  slower:  were  it  filled  with  hydro- 
gen, its  vibrations  would  be  quicker;  and  applying  the 
same  principle,  we  should  find  the  velocity  of  sound  in 
both  these  gases. 

So  likewise  the  length  of  a  solid  rod  free  at  both  ends, 
and  sounding  its  fundamental  note,  is  half  that  of  the 
sonorous  wave  in  the  substance  of  the  solid.  Hence  we 
have  only  to  determine  the  rate  of  vibration  of  such  a  rod, 
and  multiply  it  by  twice  the  length  of  the  rod,  to  obtain 
the  velocity  of  sound  in  the  substance  of  the  rod.  You 
can  hardly  fail  to  be  impressed  by  the  power  which  physi- 
cal science  has  given  us  over  these  problems;  nor  will 
you  refuse  your  admiration  to  that  famous  old  investi- 
gator, Chladni,  who  taught  us  how  to  master  them  ex- 
perimentally. 


REEDS  AND   REED-PIPES. 

The  construction  of  the  siren  and  our  experiments 
with  that  instrument  are,  no  doubt,  fresh  in  your  recol- 
lection. Its  musical  sounds  are  produced  by  the  cutting 
up  into  puffs  of  a  series  of  air-currents.  The  same  pur- 
pose is  effected  by  a  vibrating  reed,  as  employed  in  the 


EEEDS.  221 

accordion,  the  concertina,  and  the  harmonica.  In  these 
instruments  it  is  not  the  vibrations  of  the  reed  itself 
which,  imparted  to  the  air,  and  transmitted  through  it  to 
our  organs  of  hearing,  produce  the  music ;  the  function  of 
the  reed  is  constructive,  not  generative;  it  moulds  into  a 
series  of  discontinuous  puffs  that  which  without  it  would 
be  a  continuous  current  of  air. 

Reeds,  if  associated  with  organ-pipes,  sometimes  com- 
mand, and  are  sometimes  commanded  by,  the  vibrations 
of  the  column  of  air.  When  they  are  stiff  they  rule  the 
column;  when  they  are  flexible  the  column  rules  them. 
In  the  former  case,  to  derive  any  advantage  from  the  air- 
column,  its  length  ought  to  be  so  regulated  that  either  its 
fundamental  tone  or  one  of  its  overtones  shall  correspond 
to  the  rate  of  vibration  of  the  reed.  The  metal  reed 
commonly  employed  in  organ-pipes  is  shown  in  Fig.  104,  A 

v FIG.  104.  v 

\1 ^i   (j  fill'  A 


and  B,  both  in  perspective  and  in  section.  It  consists  of  a 
long  and  flexible  strip  of  metal,  v  v,  placed  in  a  rectangu- 
lar orifice,  through  which  the  current  of  air  enters  the 
pipe.  The  manner  in  which  the  reed  and  pipe  are  associ- 
ated is  shown  in  Fig.  105.  The  front,  b  c,  of  the  space 
containing  the  flexible  tongue  is  of  glass,  so  that  you  may 
see  the  tongue  within  it.  A  conical  pipe,  A  B,  surmounts 
the  reed.1  The  wire  w  i,  shown  pressing  against  the  reed, 

1  The  clear  ilhistrations  of  organ-pipes  and  reeds  introduced  here, 
and  at  p.  213,  have  been  substantially  copied  from  the  excellent  work 


222 


SOUND. 


is  employed  to  lengthen  or  shorten  it,  and  thus  to  vary  with- 
in certain  limits  its  rate  of  vibration.    At  one  time  in  the 
practice  of  music  the  reed  closed  the  aperture  by  simply 
FIG  105  falling  against  its  sides;  every  stroke  of 

the  reed  produced  a  tap,  and  these  linked 
themselves  together  to  an  unpleasant, 
screaming  sound,  which  materially  in- 
jured that  of  the  associated  organ-pipe. 
This  was  mitigated,  but  not  removed,  by 
permitting  the  reed  to  strike  against  soft 
leather;  but  the  reed  now  employed  is 
the  free  reed,  which  vibrates  to  and  fro 
between  the  sides  of  the  aperture,  al- 
most, but  not  quite,  filling  it.  In  this 
way  the  unpleasantness  referred  to  is 
avoided.  When  reed  and  pipe  synchro- 
nize perfectly,  the  sound  is  most  pure  and 
forcible;  a  certain  latitude,  however, 
is  possible  on  both  sides  of  perfect  syn- 
chronism. But  if  the  discordance  be 
pushed  too  far,  the  pipe  ceases  to  be  of 
any  use.  We  then  obtain  the  sound  due 
to  the  vibrations  of  the  reed  alone. 

Flexible  wooden  reeds,  which  can 
accommodate  themselves  to  the  require- 
ments of  the  pipes  above  them,  are  also 
employed  in  organ-pipes.  Perhaps  the 
simplest  illustration  of  the  action  of  the 
reed  commanded  by  its  aerial  column  is 
furnished  by  a  common  wheaten  straw. 
At  about  an  inch  from  a  knot,  at  r,  I 
bury  my  penknife  in  this  straw,  s  r',  Fig.  106,  to  a  depth 
of  about  one-fourth  of  the  straw's  diameter,  and,  turning 
the  blade  flat,  pass  it  upward  toward  the  knot,  thus  raif- 

of  Helmholtz.    Pipes  opening  with  hinges,  so  as  to  show  their  inner 
parts,  were  shown  in  the  lecture. 


KEED-PIPES.  223 

ing  a  strip  of  the  straw  nearly  an  inch  in  length.  This 
strip,  r  r',  is  to  be  our  reed,  and  the  straw  itself  is  to  be 
our  pipe.  It  is  now  eight  inches  long.  When  blown  into, 
it  emits  this  decidedly  musical  sound.  When  cut  so  as  to 
make  its  length  six  inches,  the  pitch  is  higher;  with  a 
length  of  four  inches,  the  pitch  is  higher  still;  and  with 
a  length  of  two  inches,  the  sound  is  very  shrill  indeed.  In 
these  experiments  the  reed  was  compelled  to  accommodate 
itself  throughout  to  the  requirements  of  the  vibrating 
column  of  air. 

The  clarionet  is  a  reed-pipe.  It  has  a  single  broad 
tongue,  with  which  a  long,  cylindrical  tube  is  associated. 
The  reed-end  of  the  instrument  is  grasped  by  the  lips,  and 
by  their  pressure  the  slit  between  the  reed  and  its  frame 
is  narrowed  to  the  required  extent.  The  overtones  of  a 
clarionet  are  different  from  those  of  a  flute.  A  flute  is  an 

FIG.  106. 


open  pipe,  a  clarionet  a  stopped  one,  the  end  at  which  the 
reed  is  placed  answering  to  the  closed  end  of  the  pipe. 
The  tones  of  a  flute  follow  the  order  of  the  natural  num- 
bers, 1,  2,  3,  4,  etc.,  or  of  the  even  numbers,  2,  4,  6,  8, 
etc. ;  while  the  tones  of  a  clarionet  follow  the  order  of  the 
odd  numbers,  1,  3,  5,  7,  etc.  The  intermediate  notes 
are  supplied  by  opening  the  lateral  orifices  of  the  instru- 
ment. Sir  C.  Wheatstone  was  the  first  to  make  known 
this  difference  between  the  flute  and  clarionet,  and  his 
results  agree  with  the  more  thorough  investigations  of 
Helmholtz.  In  the  hautboy  and  bassoon  we  have  two 
reeds  inclined  to  each  other  at  a  sharp  angle,  with  a  slit 
between  them,  through  which  the  air  is  urged.  The  pipe 
of  the  hautboy  is  conical,  and  its  overtones  are  those  of  an 
open  pipe — different,  therefore,  from  those  of  a  clarionet. 
15 


224:  SOUND. 

The  pulpy  end  of  a  straw  of  green  corn  may  be  split  by 
squeezing  it,  so  as  to  form  a  double  reed  of  this  kind,  and 
such  a  straw  yields  a  musical  tone.  In  the  horn,  trumpet, 
and  serpent,  the  performer's  lips  play  the  part  of  the  reed. 
These  instruments  are  formed  of  long,  conical  tubes,  and 
their  overtones  are  those  of  an  open  organ-pipe.  The 
music  of  the  older  instruments  of  this  class  was  limited  to 
their  overtones,  the  particular  tone  elicited  depending  on 
the  force  of  the  blast  and  the  tension  of  the  lips.  It  is 
now  usual  to  fill  the  gaps  between  the  successive  overtones 
by  means  of  keys,  which  enable  the  performer  to  vary  the 
length  of  the  vibrating  column  of  air. 

§  16.  The  Voice. 

The  most  perfect  of  reed  instruments  is  the  organ  of 
voice.  The  vocal  organ  in  man  is  placed  at  the  top  of  the 
trachea  or  windpipe,  the  head  of  which  is  adjusted  for  the 
attachment  of  certain  elastic  bands  which  almost  close  the 
aperture.  When  the  air  is  forced  from  the  lungs  through 
the  slit  which  separates  these  vocal  chords,  they  are 
thrown  into  vibration;  by  varying  their  tension,  the  rate 
of  vibration  is  varied,  and  the  sound  changed  in  pitch. 
The  vibrations  of  the  vocal  chords  are  practically  unaffect- 
ed by  the  resonance  of  the  mouth,  though  we  shall  after- 
ward learn  that  this  resonance,  by  reenforcing  one  or  the 
other  of  the  tones  of  the  vocal  chords,  influences  in  a 
striking  manner  the  quality  of  the  voice.  The  sweetness 
and  smoothness  of  the  voice  depend  on  the  perfect  closure 
of  the  slit  of  the  glottis  at  regular  intervals  during  the 
vibration. 

The  vocal  chords  may  be  illuminated  and  viewed  in  a 

mirror,  placed  suitably  at  the  back  of  the  mouth.    Varied 

experiments  of  this  kind  have  been  executed  by  Sig. 

Garcia.1     I  once  sought  to  project  the  larynx  of  M. 

1 1  owe  it  to  this  eminent  artist  to  direct  attention  to  his  experiments 


THE  VOICE.  225 

Czermak  upon  a  screen  in  this  room,  but  with  only  partial 

success.    The  organ  may,  however,  be  viewed  directly  in 

the  laryngoscope;  its  motions,  in  singing,  speaking,  and 

coughing,  being  strikingly  visible.     It  is  represented  at 

rest  in  Fig.  107.     The  roughness  of  the  voice  in  colds  is 

due,  according  to  Helmholtz,  to  mucous  flocculi,  which 

get  into  the  slit  of  the  glottis,  and  which  are  seen  by 

means  of  the  laryngoscope.    The  squeaking  falsetto  voice, 

with  which  some  persons  are  afflicted,  Helmholtz  thinks, 

may  be  produced  by  the  drawing  aside  of  the  mucous 

layer  which  ordinarily  lies  under 

and  loads  the  vocal  chords.   Their 

edges  thus  become  sharper  and 

their  weight   less;    while,   their 

elasticity    remaining    the    same, 

they  are  shaken  into  more  rapid 

tremors.      The   promptness   and 

accuracy  with  which  the  vocal 

chords  can  change  their  tension, 

their  form,  and  the  width  of  the 

slit  between  them,  to  which  must 

be  added  the  elective  resonance 

of  the  cavity  of  the  mouth,  render  the  voice  the  most 

perfect  of  musical  instruments. 

The  celebrated  comparative  anatomist,  John  Miiller, 
imitated  the  action  of  the  vocal  chords  by  means  of  bands 
of  India-rubber.  He  closed  the  open  end  of  a  glass  tube 
by  two  strips  of  this  substance,  leaving  a  slit  between 
them.  On  urging  air  through  the  slit,  the  bands  were 
thrown  into  vibration,  and  a  musical  tone  produced. 
Helmholtz  recommends  the  form  shown  in  Fig.  108,  where 
the  tube,  instead  of  ending  in  a  section  at  right  angles 
to  its  axis,  terminates  in  two  oblique  sections,  over  which 

communicated  to  the  Royal  Society  in  May,  1855,  and  recorded  in  the 
Philosophical  Magazine  for  1855,  vol.  x.,  p.  218. 


226  SOUND. 

the  bands  of  India-rubber  are  drawn.     The  easiest  mode 

of  obtaining  sounds  from  reeds  of  this  character  is  to 
roll  round  the  end  of  a  glass 
tube  a  strip  of  thin  India-rub- 
ber, leaving  about  an  inch  of 
the  substance  projecting  beyond 
the  end  of  the  tube.  Taking- 
two  opposite  portions  of  the  pro- 
jecting rubber  in  the  fingers, 
and  stretching  it,  a  slit  is 
formed,  the  blowing  through 

which  produces  a  musical  sound,  which  varies  in  pitch, 

as  the  sides  of  the  slit  vary  in  tension. 

§  17.  Vowel  Sounds. 

The  formation  of  the  vowel  sounds  of  the  human  voice 
excited  long  ago  philosophic  inquiry.  We  can  distinguish 
one  vowel  sound  from  another,  while  assigning  to  both 
the  same  pitch  and  intensity.  What,  then,  is  the  quality 
which  renders  the  distinction  possible?  In  the  year  1779 
this  was  made  a  prize  question  by  the  Academy  of  St. 
Petersburg,  and  Kratzenstein  gained  the  prize  for  the 
successful  manner  in  which  he  imitated  the  vowel  sounds 
by  mechanical  arrangements.  At  the  same  time  Von 
Kempelen,  of  Vienna,  made  similar  and  more  elaborate 
experiments.  The  question  was  subsequently  taken  up 
by  Mr.  Willis,  who  succeeded  beyond  all  his  predecessors 
in  the  experimental  treatment  of  the  subject.  The  true 
theory  of  vowel  sounds  was  first  stated  by  Sir  C.  Wheat- 
stone,  and  quite  recently  they  have  been  made  the  subject 
of  exhaustive  inquiry  by  Helmholtz.  You  will  find  little 
difficulty  in  comprehending  their  origin. 

Mounted  on  the  acoustic  bellows,  without  any  pipe 
associated  with  it,  when  air  is  urged  through  its  orifice, 
a  free  reed  speaks  in  this  forcible  manner.  When  upon 


RESONANCE  OF  THE  MOUTH.  227 

the  frame  of  the  reed  a  pyramidal  pipe  is  fixed,  you  notice 
a  change  in  the  sound;  and  by  pushing  my  flat  hand  over 
the  open  end  of  the  pipe,  the  similarity  between  the 
sound  produced  and  that  of  the  human  voice  is  unmis- 
takable. Holding  the  palm  of  the  hand  over  the  end  of 
the  pipe  so  as  to  close  it  altogether,  and  then  raising  the 
hand  twice  in  quick  succession,  the  word  "  mamma  "  is 
heard  as  plainly  as  if  it  were  uttered  by  an  infant.  For 
this  pyramidal  tube  I  now  substitute  a  shorter  one,  and 
with  it  make  the  same  experiment.  The  "  mamma " 
now  heard  is  exactly  such  as  would  be  uttered  by  a  child 
with  a  stopped  nose.  Thus,  by  associating  with  a  vi- 
brating reed  a  suitable  pipe,  we  can  impart  to  the  sound 
the  qualities  of  the  human  voice. 

In  the  organ  of  voice,  the  reed  is  formed  by  the  vocal 
chords,  and  associated  with  this  reed  is  the  resonant  cavity 
of  the  mouth,  which  can  so  alter  its  shape  as  to  resound, 
at  will,  either  to  the  fundamental  tone  of  the  vocal  chords 
or  to  any  of  their  overtones.  With  the  aid  of  the 
mouth,  therefore,  we  can  mix  together  the  fundamental 
tone  and  the  overtones  of  the  voice  in  different  propor- 
tions. Different  vowel  sounds  are  due  to  different  ad- 
mixtures of  this  kind.  Striking  one  of  this  series  of 
tuning-forks,  and  placing  it  before  my  mouth,  I  adjust 
the  size  of  that  cavity  until  it  resounds  forcibly  to  the 
fork.  Then,  without  altering  in  the  least  the  shape  or 
size  of  my  mouth,  I  urge  air  through  the  glottis.  The 
vowel  sound  "u"  (oo  in  hoop)  is  produced,  and  no  other.  I 
strike  another  fork,  and,  placing  it  in  front  of  the  mouth, 
adjust  the  cavity  to  resonance.  Then  removing  the  fork 
and  urging  air  through  the  glottis,  the  vowel  sound  "  o," 
and  it  only,  is  heard.  I  strike  a  third  fork,  adjust  my 
mouth  to  it,  and  then  urge  air  through  the  larynx;  the 
vowel  sound  ah  !  and  no  other,  is  heard.  In  all  these  cases 
the  vocal  chords  have  been  in  the  same  constant  condition. 


228  SOUND. 

They  have  generated  throughout  the  same  fundamental 
tone  and  the  same  overtones,  the  changes  of  sound  which 
you  have  heard  being  due  solely  to  the  fact  that  different 
tones  in  the  different  cases  were  reenforced  by  the  reso- 
nance of  the  mouth.  Donders  first  proved  that  the  mouth 
resounded  differently  for  the  different  vowels. 

In  the  formation  of  the  different  vowel  sounds  the 
resonant  cavity  of  the  mouth  undergoes,  according  to 
Helmholtz,  the  following  changes: 

For  the  production  of  the  sound  "  u  "  (oo  in  hoop), 
the  lips  must  be  pushed  forward,  so  as  to  make  the  cavity 
of  the  mouth  as  deep  as  possible,  and  the  orifice  of  the 
mouth,  by  the  contraction  of  the  lips,  as  small  as  possible. 
This  arrangement  corresponds  to  the  deepest  resonance  of 
which  the  mouth  is  capable.  The  fundamental  tone  itself 
of  the  vocal  chords  is  here  reenforced,  while  the  higher 
tones  retreat. 

The  vowel  "  o  "  requires  a  somewhat  wider  opening  of 
the  mouth.  The  overtones  which  lie  in  the  neighborhood 
of  the  middle  6  of  the  soprano  come  out  strongly  in  the 
case  of  this  vowel. 

When  "  Ah  "  is  sounded,  the  mouth  assumes  the  shape 
of  a  funnel,  widening  outward.  It  is  thus  tuned  to  a 
note  an  octave  higher  than  in  the  case  of  the  vowel  "  o." 
Hence,  in  sounding  "  Ah,"  those  overtones  are  most 
strengthened  which  lie  near  the  higher  &  of  the  soprano. 
As  the  mouth  is  in  this  case  wide  open,  all  the  other  over- 
tones are  also  heard,  though  feebly. 

In  sounding  "  A  "  and  "  E,"  the  hinder  part  of  the 
mouth  is  deepened,  while  the  front  of  the  tongue  rises 
against  the  gums  and  forms  a  tube;  this  yields  a  higher 
resonance-tone,  rising  gradually  from  "  A  "  to  "  E,"  while 
the  hinder  hollow  space  yields  a  lower  resonance-tone, 
which  is  deepest  when  "  E  "  is  sounded. 

These  examples  sufficiently  illustrate  the  subject  of 


VOWEL  SOUNDS.  229 

vowel  sounds.  We  may  blend  in  various  ways  the  ele- 
mentary tints  of  the  solar  spectrum,  producing  innumer- 
able composite  colors  by  their  admixture.  Out  of  violet 
and  red  we  produce  purple,  and  out  of  yellow  and  blue 
we  produce  white.  Thus  also  may  elementary  sounds  be 
blended  so  as  to  produce  all  possible  varieties  of  clang- 
tint.  After  having  resolved  the  human  voice  into  its  con- 
stituent tones,  Helmholtz  was  able  to  imitate  these  tones 
by  tuning-forks,  and,  by  combining  them  appropriately 
together,  to  produce  the  sounds  of  all  the  vowels. 

§  18.  Kundt's  Experiments:  New  Modes  of  determining 
Velocity  of  Sound. 

Unwilling  to  interrupt  the  continuity  of  our  reasonings 
and  experiments  on  the  sound  of  organ-pipes,  and  their 
relations  to  the  vibrations  of  solid  rods,  I  have  reserved 
for  the  conclusion  of  this  discourse  some  reflections  and 
experiments  which,  in  strictness,  belong  to  an  earlier 
portion  of  the  chapter.  You  have  already  heard  the 
tones,  and  made  yourselves  acquainted  with  the  various 
modes  of  division  of  a  glass  tube,  free  at  both  ends, 
when  thrown  into  longitudinal  vibration.  When  it 
sounds  its  fundamental  tone,  you  know  that  the  two 
halves  of  such  a  tube  lengthen  and  shorten  in  quick 
alternation.  If  the  tube  were  stopped  at  its  ends, 
the  closed  extremities  would  throw  the  air  within  the 
tube  into  a  state  of  vibration;  and  if  the  velocity  of 
sound  in  air  were  equal  to  its  velocity  in  glass,  the  air  of 
the  tube  would  vibrate  in  synchronism  with  the  tube 
itself.  But  the  velocity  of  sound  in  air  is  far  less  than 
its  velocity  in  glass,  and  hence,  if  the  column  of  air  is  to 
synchronize  with  the  vibrations  of  the  tube,  it  can  only  do 
so  by  dividing  itself  into  vibrating  segments  of  a  suitable 
length.  In  an  investigation  of  great  interest,  recently 
published  in  Poggendorffs  Annalen,  M.  Kundt,  of  Berlin, 


230  SOUND. 

has  taught  us  how  these  segments  may  be  rendered  visible. 
Into  this  six-foot  tube  is  introduced  the  light  powder  of 
lycopodium,  being  shaken  all  over  the  interior  surface.  A 
small  quantity  of  the  powder  clings  to  that  surface.  Stop- 
ping the  ends  of  the  tube,  holding  its  centre  by  a  fixed 
clamp,  and  sweeping  a  wet  cloth  briskly  over  one  of  its 
halves,  instantly  the  powder,  which  a  moment  ago  clung 
to  its  interior  surface,  falls  to  the  bottom  of  the  tube  in 
the  forms  shown  in  Fig.  109,  the  arrangement  of  the  lyco 

FIG.  109. 


podium  marking  the  manner  in  which  the  column  of  ail- 
has  been  divided.  Every  node  here  is  encircled  by  a  ring 
of  dust,  while  from  node  to  node  the  dust  arranges  itself 
in  transverse  streaks  along  the  ventral  segments. 

You  will  have  little  difficulty  in  seeing  that  we  perform 
here,  with  air,  substantially  the  same  experiment  as  that 
of  M.  Melde  with  a  vibrating  string.  Wh£n  the  string  was 
too  long  to  vibrate  as  a  whole,  it  met  the  requirements  of 
the  tuning-fork  to  which  it  was  attached  by  dividing 
into  ventral  segments.  Now,  in  all  cases,  the  length 
from  a  node  to  its  next  neighbor  is  half  that  of  the 
sonorous  wave:  how  many  such  half -waves  then  have  we 
in  our  tube  in  the  present  instance?  Sixteen  (the  figure 
shows  only  four  of  them).  But  the  length  of  our  glass 
tube  vibrating  thus  longitudinally  is  also  half  that  of  the 
sonorous  wave  in  glass.  Hence,  in  the  case  before  us, 
with  the  same  rate  of  vibration,  the  length  of  the  semi- 
wave  in  glass  is  sixteen  times  the  length  of  the  semi-wave 
in  air.  In  other  words,  the  velocity  of  sound  in  glass  is 
sixteen  times  its  velocity  in  air.  Thus,  by  a  single  sweep  of 
the  wet  rubber,  we  solve  a  most  important  problem.  But, 


KUNDT'S  EXPERIMENTS.  231 

as  M.  Kundt  has  shown,  we  need  not  confine  ourselves  to 
air.  Introducing  any  other  gas  into  the  tube,  a  single 
stroke  of  our  wet  cloth  enables  us  to  determine  the  rela- 
tive velocity  of  sound  in  that  gas  and  in  glass.  When 
hydrogen  is  introduced,  the  number  of  ventral  segments  is 
less  than  in  air;  when  carbonic  acid  is  introduced,  the 
number  is  greater. 

From  the  known  velocity  of  sound  in  air,  coupled  with 
the  length  of  one  of  these  dust  segments,  we  can  imme- 
diately deduce  the  number  of  vibrations  executed  in  a 
second  by  the  tube  itself.  Clasping  a  glass  tube  at  its  cen- 
tre and  drawing  my  wetted  cloth  over  one  of  its  halves,  I 
elicit  this  shrill  note.  The  length  of  every  dust  segment, 
now  within  the  tube,  is  3  inches.  Hence  the  length  of 
the  aerial  sonorous  wave  corresponding  to  this  note  is  6 
inches.  But  the  velocity  of  sound  in  air  of  our  present 
temperature  is  1,120  feet  per  second;  a  distance  which 
would  embrace  2,240  of  our  sonorous  waves.  This  num- 
ber, therefore,  expresses  the  number  of  vibrations  per 
second  executed  by  the  glass  tube  now  before  us. 

Instead  of  damping  the  centre  of  the  tube,  and  making 
it  a  nodal  point,  we  may  employ  any  other  of  its  subdi- 
visions. Laying  hold  of  it,  for  example,  at  a  point  mid- 
way between  its  centre  and  one  of  its  ends,  and  rubbing 
it  properly,  it  divides  into  three  vibrating  parts,  separated 
by  two  nodes.  We  know  that  in  this  division  the  note 
elicited  is  the  octave  of  that  heard  when  a  single  node  is 
formed  at  the  middle  of  the  tube;  for  the  vibrations  are 
twice  as  rapid.  If,  therefore,  we  divide  the  tube,  having 
air  within  it,  by  two  nodes  instead  of  one,  the  number  of 
ventral  segments  revealed  by  the  lycopodium  dust  will  be 
thirty-two  instead  of  sixteen.  The  same  remark  applies, 
of  course,  to  all  other  gases. 

Filling  a  series  of  four  tubes  with  air,  carbonic  acid, 
coal-gas,  and  hydrogen,  and  then  rubbing  each  so  as  to 


232  SOUND. 

produce  two  nodes,  M.  Kundt  found  the  number  of  dust 
segments  formed  within  the  tube  in  the  respective  cases 
to  be  as  follows: 

Air 32  dust  segments. 

Carbonic  acid  ...    40  *•     . 

Coal-gas    ....    20 

Hydrogen         ...      9 

Calling  the  velocity  in  air  unity,  the  following  frac- 
tions express  the  ratio  of  this  velocity  to  those  in  the 
other  gases: 

39 
Carbonic  acid  .        .        .    —  =  0.8 

OO 

Coal-gas   .       .       .        .    —  =  1.6 
Hydrogen         ,       .       .    ~  =  3.56 

Referring  to  a  table  introduced  in  our  first  chapter,  we 
learn  that  Dulong  by  a  totally  different  mode  of  experi- 
ment found  the  velocity  in  carbonic  acid  to  be  0.86,  and 
in  hydrogen  3.8  times  the  velocity  in  air.  The  results  of 
Dulong  were  deduced  from  the  sounds  of  organ-pipes  filled 
with  the  various  gases;  but  here,  by  a  process  of  the  ut- 
most simplicity,  we  arrive  at  a  close  approximation  to  his 
results.  Dusting  the  interior  surfaces  of  our  tubes,  filling 
them  with  the  proper  gases,  and  sealing  their  ends,  they 
may  be  preserved  for  an  indefinite  time.  By  properly 
shaking  one  of  them  at  any  moment,  its  inner  surface 
becomes  thinly  coated  with  the  dust;  and  afterward  a 
single  stroke  of  the  wet  cloth  produces  the  division  from 
which  the  velocity  of  sound  in  the  gas  may  be  immediately 
inferred. 

Savart  found  that  a  spiral  nodal  line  is  formed  round 
a  tube  or  rod  when  it  vibrates  longitudinally,  and  Seebeck 
showed  that  this  line  was  produced,  not  by  longitudinal,  but 


SOUND  FIGURES  WITHIN  TUBES.  233 

by  secondary  transverse  vibrations.  Now  this  spiral  nodal 
line  tends  to  complicate  the  division  of  the  dust  -pIQ  110 
in  our  present  experiments.  It  is,  therefore,  de- 
sirable to  operate  in  a  manner  which  shall  alto- 
gether avoid  the  formation  of  this  line ;  M.  Kundt 
has  accomplished  this,  by  exciting  the  longitudinal 
vibrations  in  one  tube,  and  producing  the  division 
into  ventral  segments  in  another,  into  which  the 
first  fits  like  a  piston.  Before  you  is  a  tube  of 
glass,  Fig.  110,  seven  feet  long,  and  two  inches 
internal  diameter.  One  end  of  this  tube  is  filled 
by  the  movable  stopper  6.  The  other  end,  K  K, 
is  also  stopped  by  a  cork,  through  the  centre  of 
which  passes  the  narrower  tube,  A  a,  which  is 
firmly  clasped  at  its  middle  by  the  cork,  K  K. 
The  end  of  the  interior  tube,  A  a,  is  also  closed 
with  a  projecting  stopper,  a,  almost  sufficient  to 
fill  the  larger  tube,  but  still  fitting  into  it  so  loose- 
ly that  the  friction  of  a  against  the  interior  sur- 
face is  too  slight  to  interfere  practically  with  its 
vibrations.  The  interior  surface  between  a  and 
&  being  lightly  coated  with  the  lycopodium  dust, 
a  wet  cloth  is  passed  briskly  over  A  K;  instantly 
the  dust  between  a  and  b  divides  into  a  number 
of  ventral  segments.  When  the  length  of  the 
column  of  air,  a  6,  is  equal  to  that  of  the  glass 
tube,  A  a,  the  number  of  ventral  segments  is  six- 
teen. When,  as  in  the  figure,  a  &  is  only  one-half 
the  length  of  A  a,  the  number  of  ventral  segments 
is-eight. 

But  here  you  must  perceive  that  the  method 
of  experiment  is  capable  of  great  extension.  In- 
stead of  the  glass  tube,  A  a,  we  may  employ  a 
rod  of  any  other  solid  substance — of  wood  or 
metal,  for  example,  and  thus  determine  the  rela- 


234:  SOUND. 

tive  velocity  of  sound  in  the  solid  and  in  air.  In  the 
place  of  the  glass  tube,  for  example,  a  rod  of  brass  of 
equal  length  may  be  employed.  Rubbing  its  external 
half  by  a  resined  cloth,  it  divides  the  column  a  &  into  the 
number  of  ventral  segments  proper  to  the  metal's  rate  of 
vibrations.  In  this  way  M.  Kundt  operated  with  brass, 
steel,  glass,  and  copper,  and  his  results  prove  the  method 
to  be  capable  of  great  accuracy.  Calling,  as  before,  the 
velocity  of  sound  in  air  unity,  the  following  numbers  ex- 
pressive of  the  ratio  of  the  velocity  of  sound  in  brass  to 
its  velocity  in  air  were  obtained  in  three  different  series  of 
experiments : 

1st  experiment 10.87 

2nd  experiment 10.87 

3rd  experiment 10.86 

The  coincidence  is  here  extraordinary.  To  illustrate 
the  possible  accuracy  of  the  method,  the  length  of  the 
individual  dust  segments  was  measured.  In  a  series  of 
twenty-seven  experiments,  this  length  was  found  to  vary 
between  43  and  44  millimetres  (each  millimetre  g^th  of 
an  inch),  never  rising  so  high  as  the  latter,  and  never  fall- 
ing so  low  as  the  former.  The  length  of  the  metal  rod, 
compared  with  that  of  one  of  the  segments  capable  of 
this  accurate  measurement,  gives  us  at  once  the  velo- 
city of  sound  in  the  metal,  as  compared  with  its  velocity 
in  air. 

Three  distinct  experiments,  performed  in  the  same 
manner  on  steel,  gave  the  following  velocities,  the  velocity 
through  air,  as  before,  being  regarded  as  unity: 

1st  experiment 15.34 

2nd  experiment 15.33 

3d  experiment      .....     15.34 

Here  the  coincidence  is  quite  as  perfect  as  in  the  case 
of  brass. 


VELOCITY  DEDUCED  FROM  SOUND  FIGURES.     235 

In  glass,  by  this  new  mode  of  experiment,  the  velocity 
was  found  to  be 

15.25.1 

Finally,  in  copper  the  velocity  was  found  to  be 
11.96. 

These  results  agree  extremely  well  with  those  obtained 
by  other  methods.  Wertheim,  for  example,  found  the 
velocity  of  sound  in  steel  wire  to  be  15.108;  M.  Kundt 
finds  it  to  be  15.34:  Wertheim.  also  found  the  velocity  in 
copper  to  be  11.17;  M.  Kundt  finds  it  to  be  11.96.  The 
differences  are  not  greater  than  might  be  produced  by 
differences  in  the  materials  employed  by  the  two  experi- 
menters. 

The  length  of  the  aerial  column  may  or  may  not  be  an 
exact  multiple  of  the  wave-length,  corresponding  to  the 
rod's  rate  of  vibration.  If  not,  the  dust  segments  usually 
take  the  form  shown  in  Fig.  111.  But  if,  by  means  of  the 

FIG.  111. 


stopper,  &,  the  column  of  air  be  made  an  exact  multiple 
of  the  wave-length,  then  the  dust  quits  the  vibrating  seg- 


FIG.  112. 


ments  altogether,  and  forms,  as  in  Fig.  112,  little  isolated 
heaps  at  the  nodes. 

1  The  velocity  in  glass  varies  with  the  quality;  the  result  of  each 
experiment  has  therefore  reference  only  to  the  particular  kind  of  glass 
employed  in  the  experiment. 


236  SOUND. 

§  19.  Explanation  of  a  Difficulty. 

And  here  a  difficulty  presents  itself.  The  stopped  end 
b  of  the  tube  Fig.  110  is,  of  course,  a  place  of  no  vibra- 
tion, where  in  all  cases  a  nodal  dust-heap  is  formed;  but, 
whenever  the  column  of  air  was  an  exact  multiple  of  the 
wave-length,  M.  Kundt  always  found  a  dust-heap  close 
to  the  end  a  of  the  vibrating  rod  also.  Thus  the  point 
from  which  all  the  vibration  emanated  seemed  itself  to  be 
a  place  of  no  vibration. 

This  difficulty  was  pointed  out  by  M.  Kundt,  but  he 
did  not  attempt  its  solution.  We  are  now  in  a  condition 
to  explain  it.  In  Lecture  III.  it  was  remarked  that  in 
strictness  a  node  is  not  a  place  of  no  vibration;  that  it  is 
a  place  of  minimum  vibration;  and  that  by  the  addition 
of  the  minute  pulses  which  the  node  permits,  vibrations 
of  vast  amplitude  may  be  produced.  The  ends  of  M. 
Kundt's  tube  are  such  points  of  minimum  motion,  the 
lengths  of  the  vibrating  segments  being  such  that,  by  the 
coalescence  of  direct  and  reflected  pulses,  the  air  at  a  dis- 
tance of  half  a  ventral  segment  from  the  end  of  the  tube 
vibrates  much  more  vigorously  than  that  at  the  end  of  the 
tube  itself.  This  addition  of  impulses  is  more  perfect  when 
the  aerial  column  is  an  exact  multiple  of  the  wave-length, 
and  hence  it  is  that,  in  this  case,  the  vibrations  become 
sufficiently  intense  to  sweep  the  dust  altogether  away  from 
the  vibrating  segments.  The  same  point  is  illustrated  by 
M.  Melde's  tuning-forks,  which,  though  they  are  the 
sources  of  all  the  motion,  are  themselves  nodes. 

An  experiment  of  Helmholtz's  is  here  capable  of  in- 
structive application.  Upon  the  string  of  the  sonometer 
described  in  our  third  lecture  I  place  the  iron  stem  of  this 
tuning-fork,  which  executes  512  complete  vibrations  in  a 
second.  At  present  you  hear  no  augmentation  of  the 
sound  of  the  fork;  the  string  remains  quiescent.  But  on 


SOLUTION  OF  A  DIFFICULTY.  237 

moving  the  fork  along  the  string,  at  the  number  33,  a 
loud,  swelling  note  issues  from  the  string.  At  this  par- 
ticular tension  the  length  33  exactly  synchronizes  with 
the  vibrations  of  the  fork.  By  the  intermediation  of  the 
string,  therefore,  the  fork  is  enabled  to  transfer  its  motion 
to  the  sonometer,  and  through  it  to  the  air.  The  sound 
continues  as  long  as  the  fork  vibrates,  but  the  least  move- 
ment to  the  right  or  to  the  left  from  this  point  causes  a 
sudden  fall  of  the  sound.  Tightening  the  string,  the  note 
disappears;  for  it  requires  a  greater  length  of  this  more 
highly  tensioned  string  to  respond  to  the  fork.  But,  on 
moving  the  fork  further  away,  at  the  number  36  the  note 
again  bursts  forth.  Tightening  still  more,  40  is  found  to 
be  the  point  of  maximum  power.  When  the  string  is 
slackened,  it  must,  of  course,  be  shortened  in  order  to  make 
it  respond  to  the  fork.  Moving  the  fork  now  toward  the 
end  of  the  string,  at  the  number  25  the  note  is  found  as 
before.  Again,  shifting  the  fork  to  35,  nothing  is  heard; 
but,  by  the  cautious  turning  of  the  key,  the  point  of  syn- 
chronism, if  I  may  use  the  term,  is  moved  further  from  the 
end  of  the  string.  It  finally  reaches  the  fork,  and  at  that 
moment  a  clear,  full  note  issues  from  the  sonometer.  In 
all  cases,  before  the  exact  point  is  attained,  and  imme- 
diately in  its  vicinity,  we  hear  "  beats,"  which,  as  we  shall 
afterward  understand,  are  due  to  the  coalescence  of  the 
sound  of  the  fork  with  that  of  the  string,  when  they  are 
nearly,  but  not  quite,  in  unison  with  each  other. 

In  these  experiments,  though  the  fork  was  the  source 
of  all  the  motion,  the  point  on  which  it  rested  was  a  nodal 
point.  It  constituted  the  comparatively  fixed  extremity 
of  the  wire,  whose  vibrations  synchronized  with  those  of 
the  fork.  The  case  is  exactly  analogous  to  that  of  the 
hand  holding  the  India-rubber  tube,  and  to  the  tuning- 
fork  in  the  experiments  of  M.  Melde.  It  is  also  an  effect 
precisely  the  same  in  kind  as  that  observed  by  M.  Kundt, 


238  SOUND. 

where  the  part  of  the  column  of  air  in  contact  with  the 
end  of  his  vibrating  rod  proved  to  be  a  node  instead  of  the 
middle  of  a  ventral  segment. 


ADDENDUM  REGARDING  RESONANCE. 

The  resonance  of  caves  and  of  rocky  inclosures  is  well 
known.  Bunsen  notices  the  thunder-like  sound  produced 
when  one  of  the  steam  jets  of  Iceland  breaks  out  near  the 
mouth  of  a  cavern.  Most  travelers  in  Switzerland  have 
noticed  the  deafening  sound  produced  by  the  fall  of  the 
Reuss  at  the  Devil's  Bridge.  The  sound  heard  when  a 
hollow  shell  is  placed  close  to  the  ear  is  a  case  of  resonance. 
Children  think  they  hear  in  it  the  sound  of  the  sea.  The 
noise  is  really  due  to  the  reenforcement  of  the  feeble 
sounds  with  which  even  the  stillest  air  is  pervaded,  and 
also  in  part  to  the  noise  produced  by  the  pressure  of  the 
shell  against  the  ear  itself.  By  using  tubes  of  different 
lengths,  the  variation  of  the  resonance  with  the  length  of 
the  tube  may  be  studied.  The  channel  of  the  ear  itself  is 
also  a  resonant  cavity.  When  a  poker  is  held  by  two 
strings,  and  when  the  fingers  of  the  hands  holding  the 
poker  are  thrust  into  the  ears,  on  striking  the  poker 
against  a  piece  of  wood,  a  sound  is  heard  as  deep  and 
sonorous  as  that  of  a  cathedral  bell.  When  open,  the 
channel  of  the  ear  resounds  to  notes  whose  periods  of 
vibration  are  about  3,000  per  second.  This  has  been 
shown  by  Helmholtz,  and  Madame  Seiler  has  found  that 
dogs  which  howl  to  music  are  particularly  sensitive  to  the 
same  notes.  We  may  expect  from  Mr.  Francis  Galton 
interesting  results  in  connection  with  this  subject. 


SUMMARY.  239 


SUMMARY  OF  CHAPTER  V. 

a  stretched  wire  is  suitably  rubbed,  in  the  di- 
rection of  its  length,  it  is  thrown  into  longitudinal  vibra- 
tions: the  wire  can  either  vibrate  as  a  whole  or  divide 
itself  into  vibrating  segments  separated  from  each  other 
by  nodes. 

*The  tones  of  such  a  wire  follow  the  order  of  the  num- 
bers 1,  2,  3,  4,  etc. 

The  transverse  vibrations  of  a  rod  fixed  at  both  ends 
do  not  follow  the  same  order  as  the  transverse  vibrations 
of  a  stretched  wire ;  for  here  the  forces  brought  into  play, 
as  explained  in  Lecture  IV.,  are  different.  But  the  longi- 
tudinal vibrations  of  a  stretched  wire  do  follow  the  same 
order  as  the  longitudinal  vibrations  of  a  rod  fixed  at  both 
ends,  for  here  the  forces  brought  into  play  are  the  same, 
being  in  both  cases  the  elasticity  of  the  material. 

A  rod  fixed  at  one  end  vibrates  longitudinally  as  a 
whole,  or  it  divides  into  two,  three,  four,  etc.,  vibrating 
parts,  separated  from  each  other  by  nodes.  The  order  of 
the  tones  of  such  a  rod  is  that  of  the  odd  numbers  1,  3,  5, 
7,  etc. 

A  rod  free  at  both  ends  can  also  vibrate  longitudinally. 
Its  lowest  note  corresponds  to  a  division  of  the  rod  into 
two  vibrating  parts  by  a  node  at  its  centre.  The  over- 
tones of  such  a  rod  correspond  to  its  division  into  three, 
four,  five,  etc.,  vibrating  parts,  separated  from  each  other 
by  two,  three,  four,  etc.,  nodes.  The  order  of  the  tones 
of  such  a  rod  is  that  of  the  numbers  1,  2,  3,  4,  5,  etc. 

We  may  also  express  the  order  by  saying  that  while 
16 


240  SOUND. 

the  tones  of  a  rod  fixed  at  both  ends  follow  the  order  of 
the  odd  numbers  1,  3,  5,  7,  etc.,  the  tones  of  a  rod  free  at 
both  ends  follow  the  order  of  the  even  numbers  2,  4,  6,  8, 
etc. 

At  the  points  of  maximum  vibration  the  rod  suffers  no 
change  of  density;  at  the  nodes,  on  the  contrary,  the 
changes  of  density  reach  a  maximum.  This  may  be 
proved  by  the  action  of  the  rod  upon  polarized  light. 

Columns  of  air  of  definite  length  resound  to  tuning- 
forks  of  definite  rates  of  vibration. 

The  length  of  a  tube  filled  with  air,  and  closed  at  one 
end,  which  resounds  to  a  fork  is  one-fourth  of  the  length 
of  the  sonorous  wave  produced  by  the  fork. 

This  resonance  is  due  to  the  synchronism  which  exists 
between  the  vibrating  period  of  the  fork  and  that  of  the 
column  of  air. 

By  blowing  across  the  mouth  of  a  tube  closed  at  one 
end,  we  produce  a  flutter  of  the  air,  and  some  pulse  of  this 
flutter  may  be  raised  by  the  resonance  of  the  tube  to  a 
musical  sound. 

The  sound  is  the  same  as  that  obtained  when  a  tuning- 
fork,  whose  rate  of  vibration  is  that  of  the  tube,  is  placed 
over  the  mouth  of  the  tube. 

TVhen  a  tube  closed  at  one  end — a  stopped  organ-pipe, 
for  example — sounds  its  lowest  note,  the  column  of  air 
within  it  is  undivided  by  a  node.  The  overtones  of  such 
a  column  correspond  to  its  division  into  parts,  like  those 
of  a  rod  fixed  at  one  end  and  vibrating  longitudinally. 
The  order  of  its  tones  is  that  of  the  odd  numbers,  1,  3,  5, 
7,  etc.  That  this  must  be  the  order  follows  from  the 
manner  in  which  the  column  is  divided. 

In  organ-pipes  the  air  is  agitated  by  causing  it  to  issue 
from  a  narrow  slit,  and  to  strike  upon  a  cutting  edge. 
Some  pulse  of  the  flutter  thus  produced  is  raised  by  the 
resonance  of  the  pipe  to  a  musical  sound. 


SUMMARY.  241 

When,  instead  of  the  aerial  flutter,  a  tuning-fork  of 
the  proper  rate  of  vibration  is  placed  at  the  embouchure 
of  an  organ-pipe,  the  pipe  speaks  in  response  to  the  fork. 
In  practice,  the  organ-pipe  virtually  creates  its  own  tun- 
ing-fork, by  compelling  the  sheet  of  air  at  its  embouchure 
to  vibrate  in  periods  synchronous  with  its  own. 

An  open  organ-pipe  yields  a  note  an  octave  higher 
than  that  of  a  closed  pipe  of  the  same  length.  This  rela- 
tion is  a  necessary  consequence  of  the  respective  modes  of 
vibration. 

When,  for  example,  a  stopped  organ-pipe  sounds  its 
deepest  note,  the  column  of  air,  as  already  explained,  is 
undivided.  When  an  open  pipe  sounds  its  deepest  note, 
the  column  is  divided  by  a  node  at  its  centre.  The  open 
pipe  in  this  case  virtually  consists  of  two  stopped  pipes 
with  a  common  base.  Hence  it  is  plain  that  the  funda- 
mental note  of  an  open  pipe  must  be  the  same  as  that  of 
a  stopped  pipe  of  half  its  length. 

The  length  of  a  stopped  pipe  is  one-fourth  that  of  the 
sonorous  wave  which  it  produces,  while  the  length  of  an 
open  pipe  is  one-half  that  of  its  sonorous  wave. 

The  order  of  the  tones  of  an  open  pipe  is  that  of  the 
even  numbers  2,  4,  6,  8,  etc.,  or  of  the  natural  numbers 
1,  2,  3,  4,  etc. 

In  both  stopped  and  open  pipes  the  number  of  vibra- 
tions executed  in  a  given  time  is  inversely  proportional 
to  the  length  of  the  pipe. 

The  places  of  maximum  vibration  in  organ-pipes  are 
places  of  minimum  changes  of  density;  while  at  the 
places  of  minimum  vibration  the  changes  of  density  reach 
a  maximum. 

The  velocities  of  sound  in  gases,  liquids,  and  solids, 
may  be 'inferred  from  the  tones  which  equal  lengths  of 
them  produce;  or  they  may  be  inferred  from  the  lengths 
of  these  substances  which  yield  equal  tones. 


242  SOUND. 

Keeds,  or  vibrating  tongues,  are  often  associated  with 
vibrating  columns  of  air.  They  consist  of  flexible  laminae, 
which  vibrate  to  and  fro  in  a  rectangular  orifice,  thus 
rendering  intermittent  the  air-current  passing  through 
the  orifice. 

The  action  of  the  reed  is  the  same  as  that  of  the 
siren. 

The  flexible  wooden  reeds  sometimes  associated  with 
organ-pipes  are  compelled  to  vibrate  in  unison  with  the 
column  of  air  in  the  pipe;  other  reeds  are  too  stiff  to  be 
thus  controlled  by  the  vibrating  air.  In  this  latter  case 
the  column  of  air  is  taken  of  such  a  length  that  its  vibra- 
tions synchronize  with  those  of  the  reed. 

By  associating  suitable  pipes  with  reeds  we  impart  to 
their  tones  the  qualities  of  the  human  voice. 

The  vocal  organ  in  man  is  a  reed  instrument,  the 
vibrating  reed  in  this  case  being  elastic  bands  placed  at 
the  top  of  the  trachea,  and  capable  of  various  degrees  of 
tension. 

The  rate  of  vibration  of  these  vocal  chords  is  practi- 
cally uninfluenced  by  the  resonance  of  the  mouth;  but 
the  mouth,  by  changing  its  shape,  can  be  caused  to  re- 
sound to  the  fundamental  tone,  or  to  any  of  the  over- 
tones of  the  vocal  chords. 

By  the  strengthening  of  particular  tones  through  the 
resonance  of  the  mouth,  the  clang-tint  of  the  voice  is 
altered. 

The  different  vowel-sounds  are  produced  by  different 
admixtures  of  the  fundamental  tone  and  the  overtones  of 
the  vocal  chords. 

When  the  solid  substance  of  a  tube  stopped  at  one,  or 
at  both  ends,  is  caused  to  vibrate  longitudinally,  the  air 
within  it  is  also  thrown  into  vibration. 

By  covering  the  interior  surface  of  the  tube  with  a 
light  powder,  the  manner  in  which  the  aerial  column  di- 


SUMMARY.  243 

rides  itself  may  be  rendered  apparent.  From  the  divis- 
ion of  the  column  the  velocity  of  sound  in  the  substance 
of  the  tube,  compared  with  its  velocity  in  air,  may  be  in- 
ferred. 

Other  gases  may  be  employed  instead  of  air,  and  the 
velocity  of  sound  in  these  gases,  compared  with  its  velocity 
in  the  substance  of  the  tube,  may  be  determined. 

The  end  of  a  rod  vibrating  longitudinally  may  be 
caused  to  agitate  a  column  of  air  contained  in  a  tube,  com- 
pelling the  air  to  divide  itself  into  ventral  segments. 
These  segments  may  be  rendered  visible  by  light  powders, 
and  from  them  the  velocity  of  sound  in  the  substance  of 
the  vibrating  rod,  compared  with  its  velocity  in  air,  may 
be  inferred. 

In  this  way  the  relative  velocities  of  sound  in  all  solid 
substances  capable  of  being  formed  into  rods,  and  of  vi- 
brating longitudinally,  may  be  determined. 


CHAPTER  VI. 

Singing  Flames. — Influence  of  the  Tube  surrounding  the  Flame. — In- 
fluence of  Size  of  Flame. — Harmonic  Notes  of  Flames. — Effect  of 
Unisonant  Notes  on  Singing  Flames.— Action  of  Sound  on  Naked 
Flames. — Experiments  with  Fish-Tail  and  Bat's- Wing  Burners. — 
Experiments  on  Tall  Flames.— Extraordinary  Delicacy  of  Flames 
as  Acoustic  Reagents.— The  Vowel-Flame.— Action  of  Conversa- 
tional Tones  upon  Flames. — Action  of  Musical  Sounds  on  Smoke- 
Jets. — Constitution  of  Water-Jets. — Plateau's  Theory  of  the  Reso- 
lution of  a  Liquid  Vein  into  Drops. — Action  of  Musical  Sounds  on 
Water-Jets.— A  Liquid  Vein  may  compete  in  Point  of  Delicacy 
with  the  Ear. 

§  1.  Rliytlim  of  Friction:  Musical  Flow  of  a  Liquid 
through  a  Small  Aperture. 

FRICTION  is  always  rhythmic.  When  a  resined  bow 
is  passed  across  a  string,  the  tension  of  the  string  se- 
cures the  perfect  rhythm  of  the  friction.  When  the 
wetted  finger  is  moved  round  the  edge  of  a  glass,  the 
breaking  up  of  the  friction  into  rhythmic  pulses  expresses 
itself  in  music.  Savart's  beautiful  experiments  on  the 
flow  of  liquids  through  small  orifices  bear  immediately 
upon  this  question.  We  have  here  the  means  of  verifying 
his  results.  The  tube  A  B,  Fig.  113,  is  filled  with  water, 
its  extremity,  B,  being  closed  by  a  plate  of  brass,  which  is 
pierced  by  a  circular  orifice  of  a  diameter  equal  to  the 
thickness  of  the  plate.  Removing  a  little  peg  which  stops 
the  orifice,  the  water  issues  from  it,  and  as  it  sinks  in  the 
tube  a  musical  note  of  great  sweetness  issues  from  the 
liquid  column.  This  note  is  due  to  the  intermittent  flow 
of  the  liquid  through  the  orifice,  by  which  the  whole 
244 


MUSICAL  FLOW  OF   WATER. 


245 


FIG.  113. 


column  above  it  is  thrown  into  vibration.  The  tendency 
to  this  effect  shows  itself  when  tea  is  poured  from  a  teapot, 
in  the  circular  ripples  that  cover  the  falling  liquid.  The 
same  intermittence  is  observed  in  the  black,  dense  smoke 
which  rolls  in  rhythmic  rings  from  the  funnel  of  a  steamer. 
The  unpleasant  noise  of  unoiled  machinery  is  also  a  decla- 
ration of  the  fact  that  the  friction  is  not  uniform,  but  is 
due  to  the  alternate  "  bite "  and 
release  of  the  rubbing  surfaces. 

Where  gases  are  concerned  fric- 
tion is  of  the  same  intermittent 
character.  A  rifle-bullet  sings  in  its 
passage  through  the  air;  while  to  the 
rubbing  of  the  wind  against  the  boles 
and  branches  of  the  trees  are  to  be 
ascribed  the  "waterfall  tones  "of  an 
agitated  pine-wood.  Pass  a  steadily- 
burning  candle  rapidly  through  the 
air;  an  indented  band  of  light,  de- 
claring intermittence,  is  often  the 
consequence,  while  the  almost  musi- 
cal sound  which  accompanies  the 
appearance  of  this  band  is  the  audi- 
ble expression  of  the  rhythm.  On 
the  other  hand,  if  you  blow  gently 
against  a  candle-flame,  the  fluttering 
noise  announces  a  rhythmic  action. 
We  have  already  learned  what  can  be  done  when  a  pipe  is 
associated  with  such  a  flutter;  we  have  learned  that  the 
pipe  selects  a  special  pulse  from  the  flutter,  and  raises  it 
by  resonance  to  a  musical  sound.  In  a  similar  manner 
the  noise  of  a  flame  may  be  turned  to  account.  The  blow- 
pipe flame  of  our  laboratory,  for  example,  when  inclosed 
within  an  appropriate  tube,  has  its  flutter  raised  to  a  roar. 
The  special  pulse  first  selected  soon  reacts  upon  the  flame 


246  SOUND. 

so  as  to  abolish  in  a  great  degree  the  other  pulses,  com- 
pelling the  flame  to  vibrate  in  periods  answering  to  the 
selected  one.  And  this  reaction  can  become  so  powerful — 
the  timed  shock  of  the  reflected  pulses  may  accumulate  to 
such  an  extent — as  to  beat  the  flame,  even  when  very 
large,  into  extinction. 

§  2.  Musical  Flames. 

Nor  is  it  necessary  to  produce  this  flutter  by  any  extra- 
neous means.  When  a  gas-flame  is  simply  inclosed  within 
a  tube,  the  passage  of  the  air  over  it  is  usually  sufficient 
to  produce  the  necessary  rhythmic  action,  so  as  to  cause 
the  flame  to  burst  spontaneously  into  song.  This  flame- 
music  may  be  rendered  exceedingly  intense.  Over  a  flame 
issuing  from  a  ring  burner  with  twenty-eight  orifices,  I 
place  a  tin  tube,  5  feet  long,  and  2£  inches  in  diameter. 
The  flame  flutters  at  first,  but  it  soon  chastens  its  impulses 
into  perfect  periodicity,  and  a  deep  and  clear  musical  tone 
is  the  result.  By  lowering  the  gas  the  note  now  sounded 
is  caused  to  cease,  but,  after  a  momentary  interval  of 
silence,  another  note,  which  is  the  octave  of  the  last,  is 
yielded  by  the  flame.  The  first  note  was  the  fundamental 
note  of  the  surrounding  tube;  this  second  note  is  its  first 
harmonic.  Here,  as  in  the  case  of  open  organ-pipes,  we 
have  the  aerial  column  dividing  itself  into  vibrating  seg- 
ments, separated  from  each  other  by  nodes. 

A  still  more  striking  effect  is  obtained  with  this  larger 
tube,  a  b,  Fig.  114,  15  feet  long,  and  4  inches  wide,  which 
was  made  for  a  totally  different  purpose.  It  is  supported 
by  a  steady  stand,  s  sf,  and  into  it  is  lifted  the  tall  burner, 
shown  enlarged  at  B.  You  hear  the  incipient  flutter: 
you  now  hear  the  more  powerful  sound.  As  the  flame  is 
lifted  higher  the  action  becomes  more  violent,  until  finally 
a  storm  of  music  issues  from  the  tube.  And  now  all  has 
suddenly  ceased;  the  reaction  of  its  own  pulses  upon 


FIG.  114. 


MUSICAL  FLAMES. 


247 


the  flame  has  beaten  it  into  extinction.  I 
relight  the  flame  and  make  it  very  small. 
When  raised  within  the  tube,  the  flame 
again  sings,  but  it  is  one  of  the  harmonics 
of  the  tube  that  you  now  hear.  On  turn- 
ing the  gas  fully  on,  the  note  ceases — all 
is  silent  for  a  moment;  but  the  storm  is 
brewing,  and  soon  it  bursts  forth,  as  at 
first,  in  a  kind  of  hurricane  of  sound. 
By  lowering  the  flame  the  fundamental 
note  is  abolished,  and  now  you  hear  the 
first  harmonic  of  the  tube.  Making  the 
flame  still  smaller,  the  first  harmonic  dis- 
appears, and  the  second  is  heard.  Your 
ears  being  disciplined  to  the  apprehension 
of  these  sounds,  I  turn  the  gas  once  more 
fully  on.  Mingling  with  the  deepest  note 
you  notice  the  harmonics,  as  if  struggling 
to  be  heard  amid  the  general  uproar  of 
the  flame.  With  a  large  Bunsen's  rose 
burner,  the  sound  of  this 
tube  becomes  powerful 
enough  to  shake  the  floor 
and  seats,  and  the  large 
audience  that  occupies 
the  seats  of  this  room, 
while  the  extinction  of 
the  flame,  by  the  re- 
action of  the  sonorous 
pulses,  announces  itself 
by  an  explosion  almost 
as  loud  as  a  pistol-shot. 
It  must  occur  to  you 
that  a  chimney  is  a  tube 
of  this  kind  upon  a  large 


248 


SOUND. 


FIG  115. 


scale,  and  that  the  roar  of  a  flame  in  a  chimney  is  simply 
a  rough  attempt  at  music% 

Let  us  now  pass  on  to  shorter  tubes  and  smaller 
flames.  Placing  tubes  of  different  lengths  over  eight 
small  flames,  each  of  them  starts  into  song,  and  you 
notice  that  as  the  tubes  lengthen  the  tones  deepen. 
The  lengths  of  these  tubes  are  so  chosen  that  they 
yield  in  succession  the  eight  notes  of  the  gamut. 
Hound  some  of  them  you  observe  a  paper  slider,  s,  Fig. 

115,  by  which  the  tube 
can  be  lengthened  or 
shortened.  If  while 
the  flame  is  sounding 
the  slider  be  raised,  the 
pitch  instantly  falls; 
if  lowered,  the  pitch 
rises.  These  experi- 
ments prove  the  flame 
to  be  governed  by  the 
tube.  By  the  reaction 
of  the  pulses,  reflected 
back  upon  the  flame, 
its  flutter  is  rendered 
perfectly  periodic,  the 
length  of  that  period 
being  determined,  as 
in  the  case  of  organ- 
pipes,  by  the  length  of 
the  tube. 

The  fixed  stars,  es- 
pecially those  near  the 
horizon,  shine  with  an 
unsteady  light,  sometimes  changing  color  as  they  twinkle. 
I  have  often  watched  at  night,  upon  the  plateaux  of  the 
Alps,  the  alternate  flash  of  ruby  and  emerald  in  the  lower 


ANALYSIS  OF  MUSICAL  FLAMES.  249 

and  larger  stars.  If  you  place  a  piece  of  looking-glass  so 
that  you  can  see  in  it  the  image  of  such  a  star,  on  tilting 
the  glass  quickly  to  and  fro,  the  line  of  light  obtained  will 
not  be  continuous,  but  will  form  a  string  of  colored  beads 
of  extreme  beauty.  The  same  effect  is  obtained  when  an 
opera-glass  is  pointed  to  the  star  and  shaken.  This  ex- 
periment sfyows  that  in  the  act  of  twinkling  the  light 
of  the  star  is  quenched  at  intervals;  the  dark  spaces 
between  the  bright  beads  corresponding  to  the  periods  of 
extinction.  Now,  our  singing  flame  is  a  twinkling  flame. 
When  it  begins  to  sing  you  observe  a  certain  quivering 
motion  which  may  be  analyzed  with  a  looking-glass,  or 
an  opera-glass,  as  in  the  case  of  the  star.1  I  can  now  see 
the  image  of  this  flame  in  a  small  looking-glass.  On  tilt- 
ing the  glass,  so  as  to  cause  the  image  to  form  a  circle 
of  light,  the  luminous  band  is  not  seen  to  be  continuous, 
as  it  would  be  if  the  flame  were  perfectly  steady;  it  is 
resolved  into  a  beautiful  chain  of  flames,  Fig.  116. 

§  3.  Experimental  Analysis  of  Musical  Flame. 

With  a  larger,   brighter,   and   less  rapidly-vibrating 
flame,    you   may    all   see    this 
intermittent  action.    Over  this  FlQ" 116> 

gas-flame,  /,  Fig.  117,  is  placed 
a  glass  tube,  A  B,  6  feet  long, 
and  2  inches  in  diameter.  The 
back  of  the  tube  is  blackened, 
so  as  to  prevent  the  light  of  the 
flame  from  falling  directly  upon 
the  screen,  which  it  is  now  de- 
sirable to  have  as  dark  as  possible.  In  front  of  the  tube 
is  placed  a  concave  mirror,  M,  which  forms  upon  the  screen 
an  enlarged  image  of  the  flame.  I  turn  the  mirror  with 

1  This  experiment  was  first  made  with  a  hydrogen-flame  by  Sir  C. 
Wheatstone. 


250 


SOUND. 


my  hand  and  cause  the  image  to  pass  over  the  screen. 
Were  the  flame  silent  and  steady,  we  should  obtain  a  con- 
tinuous band  of  light;  but  it  quivers,  and  emits  at  the 
same  time  a  deep  and  powerful  note.  On  twirling  the 


mirror,  therefore,  we  obtain,  instead  of  a  continuous  band, 
a  luminous  chain  of  images.  By  fast  turning,  these 
images  are  drawn  more  widely  apart;  by  slow  turning, 
they  are  caused  to  close  up,  the  chain  of  flames  passing 


RHYTHMIC  IGNITION  AND  EXTINCTION.          251 

through  the  most  beautiful  variations.  Clasping  the 
lower  end,  B,  of  the  tube  with  my  hand,  I  so  impede  the 
air  as  to  stop  the  fla'me's  vibration;  a  continuous  band  is 
the  consequence.  Observe  the  suddenness  with  which  this 
band  breaks  up  into  a  rippling  line  of  images  the  moment 
my  hand  is  removed,  and  the  current  of  air  is  permitted 
to  pass  over  the  flame. 

§  4.  Rate  of  Vibration  of  Flame :  Toepler's  Experiment. 

When  a  small  vibrating  coal-gas  flame  is  carefully 
examined  by  the  rotating  mirror,  the  beaded  line  is  a 
series  of  yellow-tipped  flames,  each  resting  upon  a  base  of 
the  richest  blue.  In  some  cases  I  have  been  unable  to 
observe  any  union  of  one  flame  with  another;  the  spaces 
between  the  flames  being  absolutely  dark  to  the  eye.  But 
if  dark,  the  flame  must  have  been  totally  extinguished  at 
intervals,  a  residue  of  heat,  however,  remaining  sufficient 
to  reignite  the  gas.  This  is  at  least  possible,  for  gas  may 
be  ignited  by  non-luminous  air.1  By  means  of  the  siren, 
we  can  readily  determine  the  number  of  times  this  flame 
extinguishes  and  relights  itself  in  a  second.  As  the  note 
of  the  instrument  approaches  that  of  the  flame,  unison  is 
preceded  by  these  well-known  beats,  which  become  grad- 
ually less  rapid,  and  now  the  two  notes  melt  into  perfect 
unison.  Maintaining  the  siren  at  this  pitch  for  a  minute, 
at  the  end  of  that  time  I  find  recorded  upon  our  dials 
1,700  revolutions.  But  the  disk  being  perforated  by  16 
holes,  it  follows  that  every  revolution  corresponds  to  16 
pulses.  Multiplying  1,700  by  16,  we  find  the  number  of 
pulses  in  a  minute  to  be  27,200.  This  number  of  times 
did  our  little  flame  extinguish  and  rekindle  itself  during 
the  continuance  of  the  experiment;  that  is  to  say,  it  was 
put  out  and  relighted  453  times  in  a  second. 

1  A  gas-jet,  for  example,  can  be  ignited  fire  inches  above  the  tip  of 
a  visible  gas-flame,  where  platinum-leaf  shows  no  redness. 


252  SOUND. 

A  flash  of  light,  though  instantaneous,  makes  an  im- 
pression upon  the  retina  which  endures  for  the  tenth  of  a 
second  or  more.  A  flying  rifle-bullet,  illuminated  by  a 
single  flash  of  lightning,  would  seem  to  stand  still  in  the 
air  for  the  tenth  of  a  second.  A  black  disk  with  radial 
white  strips,  when  rapidly  rotated,  causes  the  white  and 
black  to  blend  to  an  impure  gray;  while  a  spark  of  elec- 
tricity, or  a  flash  of  lightning,  reduces  the  disk  to  appar- 
ent stillness,  the  white  radial  strips  being  for  a  time 
plainly  seen.  Is^ow,  the  singing  flame  is  a  flashing  flame, 
and  M.  Toepler  has  shown  that  by  causing  a  striped  disk 
to  rotate  at  the  proper  speed  in  the  presence  of  such  a 
flame  it  is  brought  to  apparent  stillness,  the  white  stripes 
being  rendered  plainly  visible.  The  experiment  is  both 
easy  and  interesting. 

§  5.  Harmonic  Sounds  of  Flame. 

A  singing  flame  yields  so  freely  to  the  pulses  falling 
upon  it  that  it  is  almost  wholly  governed  by  the  surround- 
ing tube;  almost,  but  not  altogether.  The  pitch  of  the 
note  depends  in  some  measure  upon  the  size  of  the  flame. 
This  is  readily  proved,  by  causing  two  flames  to  emit  the 
same  note,  and  then  slightly  altering  the  size  of  either 
of  them.  The  unison  is  instantly  disturbed  by  beats.  By 
altering  the  size  of  a  flame  we  can  also,  as  already  illus- 
trated, draw  forth  the  harmonic  overtones  of  the  tube 
which  surrounds  it.  This  experiment  is  best  performed 
with  hydrogen,  its  combustion  being  much  more  vigorous 
than  that  of  ordinary  gas.  When  a  glass  tube  7  feet  long 
is  placed  over  a  large  hydrogen-flame,  the  fundamental 
note  of  the  tube  is  obtained,  corresponding  to  a  division 
of  the  column  of  air  within  it  by  a  single  node  at  the 
centre.  Placing  a  second  tube,  3  feet  6  inches  long,  over 
the  same  flame,  no  musical  sound  whatever  is  obtained; 
the  large  flame,  in  fact,  is  not  able  to  accommodate 


HISTORY  OF  SINGING  FLAMES.  £53 

itself  to  the  vibrating  period  of  the  shorter  tube.  But, 
011  lessening  the  flame,  it  soon  bursts  into  vigorous  song, 
its  note  being  the  octave  of  that  yielded  by  the  longer 
tube.  I  now  remove  the  shorter  tube,  and  once  more 
cover  the  flame  with  the  longer  one.  It  no  longer  sounds 
its  fundamental  notes,  but  the  precise  note  of  the  shorter 
tube.  To  accommodate  itself  to  the  vibrating  period  of 
the  diminished  flame,  the  longer  column  of  air  divides 
itself  like  an  open  organ-pipe  when  it  yields  its  first  har- 
monic. By  varying  the  size  of  the  flame,  it  is  possible, 
with  the  tube  now  before  you,  to  obtain  a  series  of  notes 
whose  rates  of  vibration  are  in  the  ratio  of  the  numbers 
1:2:3:4:5;  that  is  to  say,  the  fundamental  tone  and 
its  first  four  harmonics. 

These  sounding  flames,  though  probably  never  before 
raised  to  the  intensity  in  which  they  have  been  exhibited 
here  to-day,  are  of  old  standing.  In  1777,  the  sounds  of 
a  hydrogen-flame  were  heard  by  Dr.  Higgins.  In  1802, 
they  were  investigated  to  some  extent  by  Chladni,  who 
also  refers  to  an  incorrect  account  of  them  given  by  De 
Luc.  Chladni  showed  that  the  tones  are  those  of  the  open 
tube  which  surrounds  the  flame,  and  he  succeeded  in  ob- 
taining the  first  two  harmonics.  In  1802,  G.  De  la  Rive 
experimented  on  this  subject.  Placing  a  little  water  in 
the  bulb  of  a  thermometer,  and  heating  it,  he  showed  that 
musical  tones  of  force  and  sweetness  could  be  produced 
by  the  periodic  condensation  of  the  vapor  in  the  stem  of 
the  thermometer.  He  accordingly  referred  the  sounds  of 
flames  to  the  alternate  expansion  and  condensation  of  the 
aqueous  vapor  produced  by  the  combustion.  We  can 
readily  imitate  his  experiments.  Holding,  with  its  stem 
oblique,  a  thermometer-bulb  containing  water  in  the  flame 
of  a  spirit-lamp,  the  sounds  are  heard  soon  after  the  water 
begins  to  boil.  In  1818,  however,  Faraday  showed  that 
the  tones  are  produced  when  the  tube  surrounding  the 


254:  SOUND. 

flame  is  placed  in  air  of  a  temperature  higher  than  100° 
C.,  condensation  being  then  impossible.  He  also  showed 
that  the  tones  could  be  obtained  from  flames  of  carbonic 
oxide,  where  aqueous  vapor  is  entirely  out  of  the  question. 

§  6.  Action  of  Extraneous  Sounds  on  Flame:    Experi- 
ments of  Schaffgotsch  and  Tyndall. 

After  these  experiments,  the  first  novel  acoustic  ob- 
servation on  flames  was  made  in  Berlin  by  the  late  Count 
Schaffgotsch,  who  showed  that  when  an  ordinary  gas-flame 
was  surmounted  by  a  short  tube,  a  strong  falsetto  voice 
pitched  to  the  note  of  the  tube,  or  to  its  higher  octave, 
caused  the  flame  to  quiver.  In  some  cases  when  the  note 
of  the  tube  was  high,  the  flame  could  even  be  extin- 
guished by  the  voice. 

In  the  spring  of  1857,  this  experiment  came  to  my 
notice.  Xo  directions  were  given  in  the  short  account 
of  the  observation  published  in  Poggendorff's  Annalen; 
but,  in  endeavoring  to  ascertain  the  conditions  of  success, 
a  number  of  singular  effects  forced  themselves  upon  my 
attention.  Meanwhile,  Count  Schaffgotsch  also  followed 
up  the  subject.  To  a  great  extent  we  traveled  over  the 
same  ground,  neither  of  us  knowing  how  the  other  was 
engaged;  but,  so  far  as  the  experiments  then  executed 
are  common  to  us  both,  to  Count  Schaffgotsch  belongs  the 
priority. 

Let  me  here  repeat  his  first  observation.  Within  this 
tube,  11  inches  long,  burns  a  small  gas-flame,  bright  and 
silent.  The  note  of  the  tube  has  been  ascertained,  and 
now,  standing  at  some  distance  from  the  flame,  I  sound 
that  note;  the  flame  quivers.  To  obtain  the  extinction 
of  the  flame  it  is  necessary  to  employ  a  burner  with  a  very 
narrow  aperture,  from  which  the  gas  issues  under  consid- 
erable pressure.  On  gently  sounding  the  note  of  the  tube 


EXPERIMENTS  OF  SCHAFFGOTSCH  AND  TYNDALL.  255 

surrounding  such,  a  flame,  it  quivers;  but  on  throwing 
more  power  into  the  voice  the  flame  is  extinguished. 

The  cause  of  the  quivering  of  the  flame  will  be  best 
revealed  by  an  experiment  with  the  siren.  As  the  note 
of  the  siren  approaches  that  of  the  flame  you  hear  beats, 
and  at  the  same  time  you  observe  a  dancing  of  the  flame 
synchronous  with  the  beats.  The  jumps  succeed  each 
other  more  slowly  as  unison  is  approached.  They  cease 
when  the  unison  is  perfect,  and  they  begin  again  as  soon 
as  the  siren  is  urged  beyond  unison,  becoming  more  rapid 
as  the  discordance  is  increased.  The  cause  of  the  quiver 
observed  by  M.  Schaffgotsch  was  revealed  to  me.  The 
flame  jumped  because  the  note  of  the  tube  surrounding 
it  was  nearly,  but  not  quite,  in  unison  with  the  voice  of 
the  experimenter. 

That  the  jumping  of  the  flame  proceeds  in  exact  ac- 
cordance with  the  beats  fs  well  shown  by  a  tuning-fork, 
which  yields  the  same  note  as  the  flame.  Loading  such  a 
fork  with  a  bit  of  wax,  so  as  to  throw  it  slightly  out  of 
unison,  and  bringing  it,  when  agitated,  near  the  tube  in 
which  the  flame  is  singing,  the  beats  and  the  leaps  of  the 
flame  occur  at  the  same  intervals.  When  the  fork  is 
placed  over  a  resonant  jar,  all  of  you  can  hear  the  beats, 
and  see  at  the  same  time  the  dancing  of  the  flame.  By 
changing  the  load  upon  the  tuning-fork,  or  by  slightly 
altering  the  size  of  the  flame,  the  rate  at  which  the  beats 
succeed  each  other  may  be  altered;  but  in  all  cases  the 
jumps  address  the  eye  at  the  moments  when  the  beats 
address  the  ear. 

While  executing  these  experiments,  I  noticed  that,  on 
raising  my  voice  to  the  proper  pitch,  a  flame  which  had 
been  burning  silently  in  its  tube  began  to  sing.  The  same 
observation  had,  without  my  knowledge,  been  made  a 
short  time  previously  by  Count  Schaffgotsch.  A  tube,  12 
inches  long,  is  placed  over  this  flame,  which,  occupies  a 
17 


256  SOUND. 

position  about  an  inch  and  a  half  from  the  lower  end  of 
the  tube.  When  the  proper  note  is  sounded  the  flame 
trembles,  but  it  does  not  sing.  When  the  tube  is  lowered 
until  the  flame  is  three  inches  from  its  end,  the  song  is 
spontaneous.  Between  these  two  positions  there  is  a 
third,  at  which,  if  the  flame  be  placed,  it  will  burn  si- 
lently; but  if  it  be  excited  by  the  voice  it  will  sing,  and 
continue  to  sing. 

Even  when  the  back  is  turned  toward  the  flame  the 
sonorous  pulses  run  round  the  body,  reach  the  tube,  and 
call  forth  the  song.  A  pitch-pipe,  or  any  other  instrument 
which  yields  a  note  of  the  proper  height,  produces  the 
same  effect.  Mounting  a  series  of  tubes,  capable  of  emit- 
ting all  the  notes  of  the  gamut,  over  suitable  flames,  with 
an  instrument  sufficiently  powerful,  and  from  a  distance 
of  20  or  30  yards,  a  musician,  by  running  over  the  scale, 
might  call  forth  all  the  notes  in  succession,  the  whole  series 
of  flames  finally  joining  in  the  song. 

When  a  silent  flame,  capable  of  being  excited  in  the 
manner  here  described,  is  looked  at  in  a  moving  mirror,  it 
produces  there  a  continuous  band  of  light.  Nothing  can 
be  more  beautiful  than  the  sudden  breaking  up  of  this 
band  into  a  string  of  richly-luminous  pearls  at  the  instant 
the  voice  is  pitched  to  the  proper  note. 

One  singing  flame  may  be  caused  to  effect  the  musical 
ignition  of  another.  Before  you  are  two  small  flames,  f 
and  /,  Fig.  118,  the  tube  over  /'  being  10^  inches,  and 
that  over  f  12  inches  long.  The  shorter  tube  is  clasped 
by  a  paper  slider,  s.  The  flame  f  is  now  singing,  but  the 
flame  /,  in  the  longer  tube,  is  silent.  I  raise  the  paper 
slider  which  surrounds  f,  so  as  to  lengthen  the  tube, 
and  on  approaching  the  pitch  of  the  tube  surrounding  /, 
that  flame  sings.  The  experiment  may  be  varied  by 
making  f  the  singing  flame  and  f  the  silent  one  at  start- 
ing. Raising 'the  telescopic  slider,  a  point  is  soon  attained 


SENSITIVE  FLAMES.  257 

where  the  flame  /'  commences  its  song.    In  this  way  one 
flame  may  excite  another  through  considerable  distances. 


FIG.  118. 


It  is  also  possible  to  silence  the  singing  flame  by  the 
proper  management  of  the  voice. 


SENSITIVE  NAKED  FLAMES. 
§  Y.  Discovery  of  Sensitive  Flames  by  Le  Conte. 

We  have  hitherto  dealt  with  flames  surrounded  by 
resonant  tubes;  and  none  of  these  flames,  if  naked,  would 
respond  in  any  way  to  such  noise  or  music  as  could  be 
here  applied.  Still  it  is  possible  to  make  naked  flames 
thus  sympathetic.  This  action  of  musical  sounds  upon 


258  SOUND. 

naked  flames  was  first  observed  by  Prof.  Le  Conte  at  a 
musical  party  in  the  United  States.  His  observation  is 
thus  described:  "  Soon  after  the  music  commenced,  I 
observed  that  the  flame  exhibited  pulsations  which  were 
exactly  synchronous  with  the  audible  beats.  This  phe- 
nomenon was  very  striking  to  every  one  in  the  room,  and 
especially  so  when  the  strong  notes  of  the  violoncello 
came  in.  It  was  exceedingly  interesting  to  observe  how 
perfectly  even  the  trills  of  this  instrument  were  reflected 
on  the  sheet  of  flame.  A  deaf  man  might  have  seen  the 
"harmony.  As  the  evening  advanced,  and  the  diminished 
consumption  of  gas  in  the  city  increased  the  pressure,  the 
phenomenon  became  more  conspicuous.  The  jumping  of 
the  flame  gradually  increased,  became  somewhat  irregular, 
and,  finally,  it  began  to  flare  continuously,  emitting  the 
characteristic  sound,  indicating  the  escape  of  a  greater 
amount  of  gas  than  could  be  properly  consumed.  I  then 
ascertained,  by  experiment,  that  the  phenomenon  did  not 
take  place  unless  the  discharge  of  gas  was  so  regulated 
that  the  flame  approximated  to  the  condition  of  flaring.  I 
likewise  determined,  by  experiment,  that  the  effects  were 
not  produced  by  jarring  or  shaking  the  floor  and  walls  of 
the  room  by  means  of  repeated  concussions.  Hence  it  is 
obvious  that  the  pulsations  of  the  flame  were  not  owing  to 
indirect  vibrations  propagated  through  the  medium  of  the 
walls  of  the  room  to  the  burning-apparatus,  but  must  have 
been  produced  by  the  direct  influence  of  aerial  sonorous 
pulses  on  the  burning  jet."  * 

The  significant  remark,  that  the  jumping  of  the  flame 

1  Philosophical  Magazine,  March,  1858,  p.  235.  In  the  Appendix 
Prof.  Le  Conte's  interesting  paper  is  given  in  extenso.  Some  years 
subsequently  Mr.  (now  Professor)  Barrett,  while  preparing  some  experi- 
ments for  my  lectures,  observed  the  action  of  a  musical  sound  upon  a 
flame,  and  by  the  selection  of  suitable  burners  he  afterward  succeeded 
in  rendering  the  flame  extremely  sensitive.  Le  Conte,  of  whose  dis- 
covery I  informed  Mr.  Barrett,  was  my  own  starting-point. 


SENSITIVENESS  OF  A  CANDLE-FLAME. 


259 


was  not  observed  until  it  was  near  flaring,  suggests  the 
means  of  repeating  the  experiments  of  Dr.  Le  Conte; 
while  a  more  intimate  knowledge  of  the  conditions  of  suc- 
cess enables  us  to  vary  and  exalt  them  in  a  striking  degree. 
Before  you  burns  a  bright  candle-flame,  but  no  sound  that 
can  be  produced  here  has  any  effect  upon  it.  Though 
sonorous  waves  of  great  power  be  sent  through  the  air,  the 
candle-flame  remains  insensible. 

But  by  proper  precautions  even  a  candle-flame  may  be 
rendered  sensitive.  Urging  from  a  small  blow-pipe  a 
narrow  stream  of  air  through  such  a  flame,  an  incipient 
flutter  is  produced.  The  flame  then  jumps  visibly  to  the 
sound  of  a  whistle,  or  to  a  chirrup.  The  experiment  may 
be  so  arranged  that,  when  the  whistle  sounds,  the  flame 
shall  be  either  restored  almost  to  its  pristine  brightness, 
or  that  the  small  amount  of  light  it  still  possesses  shall 
disappear. 

The  blow-pipe  flame  of  our  laboratory  is  totally  un- 
affected by  the  sound  of  the  whistle  as  long  as  no  air  is 
urged  through  it.  By  properly  tempering  the  force  of 
the  blast,  a  flame  is  obtained  of  the  shape  shown  in  Fig. 
FIG.  119. 


FIG.  120. 


119.  On  sounding  the  whistle  the  erect  portion  of  the 
flame  drops  down,  and  while  the  sound  continues  the 
flame  maintains  the  form  shown  in  Fig.  120. 


260  SOUND. 

§  8.  Experiments  on  Fish-tail  and  Bat's-wing  Flames. 

We  now  pass  on  to  a  thin  sheet  of  flame,  issuing  from 
a  common  fish-tail  burner,  Fig.  121.  You  might  sing  to 
this  flame,  varying  the  pitch  of  your  voice,  no  shiver  of 
the  flame  would  be  visible.  You  might  employ  pitch- 

FIG.  122. 


FIG.  121. 


pipes,  tuning-forks,  bells,  and  trumpets,  with  a  like  ab- 
sence of  all  effect.  A  barely  perceptible  motion  of  the 
interior  of  the  flame  may  be  noticed  when  a  shrill  whistle 
is  blown  close  to  it.  But  by  turning  the  cock  more  fully 
on,  the  flame  is  brought  to  the  verge  of  flaring.  And  now, 
when  the  whistle  is  blown,  the  flame  thrusts  suddenly  out 
seven  quivering  tongues,  Fig.  122.  The  moment  the 
sound  ceases,  the  tongues  disappear,  and  the  flame  be- 
comes quiescent. 

Passing  from  a  fish-tail  to  a  bat's-wing  burner,  we 
obtain  a  broad,  steady  flame,  Fig.  123.    It  is  quite  insen- 
sible to  the  loudest  sound  which  would  be  tolerable  here. 
The  flame  is  fed  from  a  small  gas-holder.1     Increasing 
1  A  gas-bag  properly  weighted  also  answers  for  these  experiments. 


BAT'S-WING  FLAMES. 


261 


gradually  the  pressure,  a  slight  flutter  of  the  edge  of  the 
flame  at  length  answers  to  the  sound  of  the  whistle.  Turn- 
ing on  the  gas  until  the  flame  is  on  the  point  of  roaring, 
and  blowing  the  whistle,  it  roars,  and  suddenly  assumes 
the  form  shown  in  Fig.  124. 

When  a  distant  anvil  is  struck  with  a  hammer,  the 
flame  instantly  responds  by  thrusting  forth  its  tongues. 

An  essential  condition  to  entire  success  in  these  experi- 

FIG.  124. 


ments  disclosed  itself  in  the  following  manner:  I  was 
operating  on  two  fish-tail  flames,  one  of  which  jumped  to 
a  whistle  while  the  other  did  not.  The  gas  of  the  non- 
sensitive  flame  was  turned  off,  additional  pressure  being 
thereby  thrown  upon  the  other  flame.  It  flared,  and  its 
cock  was  turned  so  as  to  lower  the  flame;  but  it  now 
proved  non-sensitive,  however  close  it  might  be  brought  to 
the  point  of  flaring.  The  narrow  orifice  of  the  half-turned 
cock  interfered  with  the  action  of  the  sound.  When  the 
gas  was  turned  fully  on,  the  flame  being  lowered  by  open- 
ing the  cock  of  the  other  burner,  it  became  again  sensi- 
tive. Up  to  this  time  a  great  number  of  burners  had 
been  tried,  but  with  many  of  them  the  action  was  nil. 
Acting,  however,  upon  the  hint  conveyed  by  this  observa- 


262  SOUND.     . 

tion,  the  cocks  which  fed  the  flames  were  more  widely 
opened,  and  our  most  refractory  burners  thus  rendered 
sensitive. 

In  this  way  the  observation  of  Dr.  Le  Conte  is  easily 
and  strikingly  illustrated;  in  our  subsequent,  and  far  more 
delicate  experiments,  the  precaution  just  referred  to  is  still 
more  essential. 

§  9.  Experiments  on  Flames  from  Circular  Apertures. 

A  long  flame  may  be  shortened  and  a  short  one  length- 
ened, according  to  circumstances,  by  sonorous  vibrations. 
The  flame  shown  in  Fig.  125  is  long,  straight,  and  smoky; 
that  in  Fig.  126  is  short,  forked,  and  brilliant.  On  sound- 

Fio.  128. 
FIG.  125.  jOL.       FIG.  129. 


ing  the  whistle,  the  long  flame  becomes  short,  forked,  and 
brilliant,  as  in  Fig.  127;  while  the  forked  flame  becomes 


TALL  FLAMES.  263 

long  and  smoky,  as  in  Fig.  128.  As  regards,  therefore, 
their  response  to  the  sound  of  the  whistle,  one  of  these 
flames  is  the  complement  of  the  other. 

In  Fig.  129  is  represented  another  smoky  flame  which, 
when  the  whistle  sounds,  breaks  up  into  the  form  shown 
in  Fig.  130. 

When  a  brilliant  sensitive  flame  illuminates  an  other- 
wise dark  room,  in  which  a  suitable  bell  is  caused  to  strike, 
a  series  of  periodic  quenchings  of  the  light  by  the  sound 
occurs.  Every  stroke  of  the  bell  is  accompanied  by  a  mo- 
mentary darkening  of  the  room. 

The  foregoing  experiments  illustrate  the  lengthening 
and  shortening  of  flames  by  sonorous  vibrations.  They 
may  also  produce  rotation.  From  some  of  our  home-made 
burners  issue  flat  flames,  about  ten  inches  high,  and  three 
inches  across  at  their  widest  part.  When  the  whistle 
sounds,  the  plane  of  each  flame  turns  ninety  degrees  round, 
and  continues  in  its  new  position  as  long  as  the  sound 
continues. 

A  flame  of  admirable  steadiness  and  brilliancy  now 
burns  before  you.  It  issues  from  a  single  circular  orifice 
in  a  common  iron  nipple.  This  burner,  which  requires 
great  pressure  to  make  its  flame  flare,  has  been  specially 
chosen  for  the  purpose  of  enabling  you  to  observe,  with 
distinctness,  the  gradual  change  from  apathy  to  sensitive- 
ness. The  flame,  now  4  inches  high,  is  quite  indifferent 
to  sound.  On  increasing  the  pressure  its  height  becomes 
6  inches;  but  it  is  still  indifferent.  When  its  length  is  12 
inches,  a  barely  perceptible  quiver  responds  to  the  whistle. 
When  16  or  IT  inches  high,  it  jumps  briskly  the  moment 
an  anvil  is  tapped  or  the  whistle  sounded.  When  the 
flame  is  20  inches  long  you  observe  a  quivering  at  inter- 
vals, which  announces  that  it  is  near  roaring.  A  slight 
increase  of  pressure  causes  it  to  roar,  and  shorten  at  the 
same  time  to  8  inches. 


264  SOUND. 

Diminishing  the  pressure  a  little,  the  flame  is  again 
20  inches  long,  but  it  is  on  the  point  of  roaring  and  short- 
ening. Like  the  singing  flames  which  were  started  by 
the  voice,  it  stands  on  the  brink  of  a  precipice.  The 
proper  note  pushes  it  over.  It  shortens  when  the  whistle 
sounds,  exactly  as  it  did  when  the  pressure  is  in  excess. 
The  action  reminds  one  of  the  story  of  the  Swiss  mule- 
teers, who  are  said  to  tie  up  their  bells  at  certain  places 
lest  the  tinkle  should  bring  an  avalanche  down.  The 
snow  must  be  very  delicately  poised  before  this  could  oc- 
cur. It  probably  never  did  occur,  but  our  flame  illus- 
trates the  principle.  We  bring  it  to  the  verge  of  falling, 
and  the  sonorous  pulses  precipitate  what  was  already  im- 
minent. This  is  the  simple  philosophy  of  all  these  sensi- 
tive flames. 

When  the  flame  flares,  the  gas  in  the  orifice  of  the 
burner  is  in  a  state  of  vibration;  conversely,  when  the 
gas  in  the  orifice  is  thrown  into  vibration,  the  flame,  if 
sufficiently  near  the  flaring  point,  will  flare.  Thus  the 
sonorous  vibrations,  by  acting  on  the  gas  in  the  passage  of 
the  burner,  become  equivalent  to  an  augmentation  of 
pressure  in  the  holder.  In  fact,  we  have  here  revealed  to 
us  the  physical  cause  of  flaring  through  excess  of  pressure, 
which,  common  as  it  is,  has  never  been  hitherto  explained. 
The  gas  encounters  friction  in  the  orifice  of  the  burner, 
which,  when  the  force  of  transfer  is  sufficiently  great, 
throws  the  issuing  stream  into  the  state  of  vibration  that 
produces  flaring.  It  is  because  the  flaring  is  thus  caused, 
that  an  infinitesimal  amount  of  energy  in  the  form  of 
vibrations  of  the  proper  period  can  produce  an  effect 
equivalent  to  a  considerable  increase  of  pressure. 

§  10.  Seat  of  Sensitiveness. 

That  the  external  vibrations  act  upon  the  gas  in  the 
orifice  of  the  burner,  and  not  first  upon  the  burner  itself, 


SEAT  OF  SENSITIVENESS. 


the  tube  leading  to  it,  or  the  flame  above  it,  is  thus 
proved.  A  glass  funnel  K,  Fig.  131,  is  attached  to  a  tube 
3  feet  long,  and  half  an  inch  in  diameter.  A  sensitive 
flame  &  is  placed  at  the  open  end  T  of  the  tube,  while  a 
small  high-pitched  reed  is  placed  in  the  funnel  at  K. 
FIG.  131. 


When  the  sound  is  converged  upon  the  root  of  the  flame, 
as  in  Fig.  131,  the  action  is  violent;  when  converged  on  a 
point  half  an  inch  above  the  burner,  as  in  Fig.  132,  or  at 

FIG.  133.  FIG.  133. 


half  an  inch  below  the  burner,  as  in  Fig.  133,  there  is  no 
action.     The  glass  tube  may  be  dispensed  with  and  the 


266  SOUND. 

funnel  alone  employed,  if  care  be  taken  to  screen  off  all 
sound  save  that  which  passes  through  the  shank  of  the 
funnel.1 

§  11.  Influence  of  Pitch. 

All  sounds  are  not  equally  effective  on  flie  flame; 
waves  of  special  periods  are  required  to  produce  the  maxi- 
mum effect.  The  effectual  periods  are  those  which  syn- 
chronize with  the  waves  produced  by  the  friction  of  the 
gas  itself  against  the  sides  of  its  orifice.  AVith  some  of 
these  flames  a  low  deep  whistle  is  more  effective  than  a 
shrill  one.  With  others  the  exciting  tremors  must  be 
very  rapid,  and  the  sound  consequently  shrill.  Not  one 
of  these  four  tuning-forks,  which  vibrate  256  times,  320 
times,  384  times,  and  512  times  respectively  in  a  second, 
has  any  effect  upon  the  flame  from  our  iron  nipple.  But, 
besides  their  fundamental  tones,  these  forks,  as  you  know, 
can  be  caused  to  yield  a  series  of  overtones  of  very  high 
pitch.  The  vibrations  of  this  series  are  1,600,  2,000, 
2,400,  and  3,200  per  second,  respectively.  The  flame 
jumps  in  response  to  each  of  these  sounds;  the  response 
to  that  of  the  highest  pitch  being  the  most  prompt  and 
energetic  of  all. 

To  the  tap  of  a  hammer  upon  a  board  the  flame  re- 
sponds; but  to  the  tap  of  the  same  hammer  upon  an  anvil 
the  response  is  much  more  brisk  and  animated.  The 
reason  is,  that  the  clang  of  the  anvil  is  rich  in  the  higher 
tones  to  which  the  flame  is  most  sensitive.  The  powerful 
tone  obtained  when  our  inverted  bell  is  reenforced  by  its 
resonant  tube  has  no  power  over  this  flame.  But  when  a 
halfpenny  is  brought  into  contact  with  the  vibrating  sur- 
face the  flame  instantly  shortens,  flutters,  and  roars.  I 

1  In  the  actions  described  in  the  case  of  the  blow-pipe  and  candle 
flames,  it  was  the  jet  of  air  issuing  from  the  blow-pipe,  and  not  the 
flame  itself,  that  was  directly  acted  on  by  the  external  vibrations. 


INFLUENCE  OF  PITCH. 


267 


send  an  assistant  with  a  smaller  bell,  worked  by  clock-work, 
to  the  most  distant  part  of  the  gallery.    He  there  detaches 
the  hammer;  the  strokes  follow  each  other  in  rhythmic 
succession,  and  at  every  stroke  the  flame  FIG.  134.  FIG.  135. 
falls  from  a  height  of  20  to  a  height  of  8 
inches,  roaring  as  it  falls. 

The  rapidity  with  which  sound  is  prop- 
agated through  air  is  well  illustrated  by 
these  experiments.  There  is  no  sensible 
interval  between  the  stroke  of  the  bell 
and  the  ducking  of  the  flame. 

When  the  sound  acting  on  the  flame 
is  of  very  short  duration  a  curious  and 
instructive  effect  is  observed.  The  sides 
of  the  flame  half-way  down,  and  lower,  ^ 

are  seen  suddenly  fringed  by  luminous  V 

tongues,  the  central  flame  remaining  ap- 
parently undisturbed  in  both  height  and 
thickness.  The  flame  in  its  normal  state 
is  shown  in  Fig.  134,  and  with  its  fringes 
in  Fig.  135.  The  effect  is  due  to  the  re- 
tention of  the  impression  upon  the  retina. 
The  flame  actually  falls  as  low  as  the 
fringes,  but  its  recovery  is  so  quick  that 
to  the  eye  it  does  not  appear  to  shorten  at  all.1 

§  12.  The  Vowel-flame. 

A  flame  of  astonishing  sensitiveness  now  burns  before 
you.  It  issues  from  the  single  orifice  of  a  steatite  burner, 
and  reaches  a  height  of  24  inches.  The  slightest  tap  on 

1  Numerous  modifications  of  these  experiments  are  possible.  Other 
inflammable  gases  than  coal-gas  may  be  employed.  Mixtures  of  gases 
have  also  been  found  to  yield  beautiful  and  striking  results.  An  in- 
finitesimal amount  of  mechanical  impurity  has  been  found  to  exert  a 
powerful  influence. 


268  SOUND. 

a  distant  anvil  reduces  its  height  to  7  inches.  When  a 
bunch  of  keys  is  shaken  the  flame  is  violently  agitated, 
and  emits  a  loud  roar.  The  dropping  of  a  sixpence  into  a 
hand  already  containing  coin,  at  a  distance  of  20  yards, 
knocks  the  flame  down.  It  is  not  possible  to  walk  across 
the  floor  without  agitating  the  flame.  The  creaking  of 
boots  sets  it  in  violent  commotion.  The  crumpling,  or 
tearing  of  paper,  or  the  rustle  of  a  silk  dress,  does  the 
same.  It  is  startled  by  the  patter  of  a  rain-drop.  I  hold 
a  watch  near  the  flame:  nobody  hears  its  ticks;  but  you 
all  see  their  effect  upon  the  flame.  At  every  tick  it  falls 
and  roars.  The  winding  up  of  the  watch  also  produces 
tumult.  The  twitter  of  a  distant  sparrow  shakes  the 
flame;  the  note  of  a  cricket  would  do  the  same.  A  chir- 
rup from  a  distance  of  30  yards  causes  it  to  fall  and  roar. 
I  repeat  a  passage  from  Spenser: 

"  Her  ivory  forehead  full  of  bounty  brave, 
Like  a  broad  table  did  itself  dispread ; 
For  love  his  lofty  triumphs  to  engrave, 

And  write  the  battles  of  his  great  godhead. 
All  truth  and  goodness  might  therein  be  read, 

For  there  their  dwelling  was,  and  when  she  spake, 
Sweet  words,  like  dropping  honey  she  did  shed ; 

And  through  the  pearls  and  rubies  softly  brake 
A  silver  sound,  which  heavenly  music  seemed  to  make." 

The  flame  selects  from  the  sounds  those  to  which  it  can 
respond.  It  notices  some  by  the  slightest  nod,  to  others 
it  bows  more  distinctly,  to  some  its  obeisance  is  very 
profound,  while  to  many  sounds  it  turns  an  entirely  deaf 
ear. 

In  Fig.  136,  this  wonderful  flame  is  represented.  On 
chirruping  to  it,  or  on  shaking  a  bunch  of  keys  within  a 
few  yards  of  it,  it  falls  to  the  size  shown  in  Fig.  137,  the 
whole  length,  a  6,  of  the  flame  being  suddenly  abolished. 
The  light  at  the  same  time  is  practically  destroyed,  a  pale 
and  almost  non-luminous  residue  of  it  alone  remain- 


THE  VOWEL-FLAME.  269 

ing.     These  figures  are  taken  from  photographs  of  the 

flame. 

To  distinguish  it  from  the  others  I  have  called  this 

FIG.  136.  the  "  vowel-flame,"  because  the  different  vowel- 
sounds  affect  it  differently.  A  loud  and  sonorous 
u  does  not  move  the  flame;  on  changing  the 
sound  to  o,  the  flame  quivers;  when  E  is  sounded, 
the  flame  is  strongly  affected.  I  utter  the  words 
boot,  boat,  and  beat,  in  succession.  To  the  first 
there  is  no  response;  to  the  second,  the  flame 
starts;  by  the  third  is  thrown  into  greater  com- 
motion; the  sound  Ah!  is  still  more  powerful. 
Did  we  not  know  the  constitution  of  vowel-sounds 
this  deportment  would  be  an  insoluble  enigma. 
As  it  is,  however,  the  flame  illustrates  the  theory 
of  vowel-sounds.  It  is  most  sensitive  to  sounds 
of  high  pitch;  hence  we  should  infer  that  the 
sound  Ah!  contains  higher  notes  than  the  sound 
E;  that  E  contains  higher  notes  than  o;  and  o 
higher  notes  than  u.  I  need  not  say  that 

FTP   1 ^7 

this  agrees  perfectly  with  the  analysis  of 
Helmholtz. 

This  flame  is  peculiarly  sensitive  to 
the  utterance  of  the  letter  s.  A  hiss 
contains  the  elements  that  most  forcibly 
affect  the  flame.  The  gas  issues  from  its 
burner  with  a  hiss,  and  an  external  sound 
of  this  character  is  therefore  exceedingly 
effective.  From  a  metal  box  containing 
compressed  air  I  allow  a  puff  to  escape; 
the  flame  instantly  ducks  down  not  by 
any  transfer  of  air  from  the  box  to  the 
flame,  for  the  distance  between  both  utterly  excludes  this 
idea — it  is  the  sound  that  affects  the  flame.  From  the 
most  distant  part  of  the  gallery  my  assistant  permits  the 


270 


SOUND. 


compressed  air  to  issue  in  puffs  from  the  box;  at  every 
puff  the  flame  suddenly  falls.  The  hiss  of  the  issuing  air 
at  the  one  orifice  precipitates  the  tumult  of  the  flame  at 
the  other. 

When  a  musical-box  is  placed  on  the  table,  and  per- 
mitted to  play,  the  flame  behaves  like  a  sentient  and 
motor  creature — bowing  slightly  to  some  tones,  and  cour- 
tesying  deeply  to  others. 

§  13.  Mr.  Philip  Barry's  Sensitive  Flame. 

Mr.  Philip  Barry  has  discovered  a  new  and  very  effec- 
tive form  of  sensitive  flame,  which  he  thus  describes  in  a 
letter  to  myself:  "It  is  the  most  sensitive  of  all  the 
flames  that  I  am  acquainted  with,  though  from  its  smaller 
size  it  is  not  so  striking  as  your  vowel  flame.  It  possesses 
the  advantage  that  the  ordinary 
pressure  in  the  gas-mains  is  quite 
sufficient  to  produce  it.  The 
method  of  producing  it  consists  in 
igniting  the  gas  (ordinary  coal- 
gas)  not  at  the  burner  but  some 
inches  above  it,  by  interposing  be- 
tween the  burner  and  the  flame  a 
piece  of  wire-gauze." 

I  give  a  sketch  of  the  arrange- 
ment adopted,  Fig.  138.  The  space 
between  the  burner  and  gauze  was 
2  inches.  The  gauze  was  about  7 
inches  square,  resting  on  the  ring 
of  a  retort-stand.  It  had  32 
meshes  to  the  lineal  inch.  The 
burner  was  Sugg's  steatite  pinhole  burner,  the  same  as 
used  for  the  vowel-flame. 

The  flame  is  a  slender  cone  about  four  inches  high, 
the  upper  portion  giving  a  bright-yellow  light,  the  base 


BARRY'S  FLAME.  271 

being  a  non-luminous  blue  flame.  At  the  least  noise  this 
flame  roars,  sinking  down  to  the  surface  of  the  gauze,  be- 
coming at  the  same  time  invisible.  It  is  very  active  in 
its  responses,  and,  being  rather  a  noisy  flame,  its  sympathy 
is  apparent  to  the  ear  as  well  as  the  eye. 

"  To  the  vowel-sounds  it  does  not  appear  to  answer 
so  discriminately  as  the  vowel-flame.  It  is  extremely 
sensitive  to  A,  very  slightly  to  E,  more  so  to  i,  entirely 
non-sensitive  to  o,  but  slightly  sensitive  to  u. 

"  It  dances  in  the  most  perfect  manner  to  a  small 
musical  snuff-box,  and  is  highly  sensitive  to  most  of  the 
sonorous  vibrations  which  affect  the  vowel-flames." 


§  14.  Sensitive  Smoke-jets. 

It  is  not  to  the  flame,  as  such,  that  we  owe  the  ex- 
traordinary phenomena  which  have  been  just  described. 
Effects  substantially  the  same  are  obtained  when  a  jet  of 
unignited  gas,  of  carbonic  acid,  hydrogen,  or  even  air  it- 
self, issues  from  an  orifice  under  proper  pressure.  None  of 
these  gases,  however,  can  be  seen  in  its  passage  through 
air,  and,  therefore,  we  must  associate  with  them  some 
substance  which,  while  sharing  their  motions,  will  reveal 
them  to  the  eye.  The  method  employed  from  time  to 
time  in  this  place  of  rendering  aerial  vortices  visible  is 
well  known  to  many  of  you.  By  tapping  a  membrane 
which  closes  the  mouth  of  a  large  funnel  filled  with 
smoke,  we  obtain  beautiful  smoke-rings,  which  reveal  the 
motion  of  the  air.  By  associating  smoke  with  our  gas- 
jets,  in  the  present  instance,  we  can  also  trace  their  course, 
and,  when  this  is  done,  the  unignited  gas  proves  as  sensi- 
tive as  the  flames.  The  smoke-jets  jump,  shorten,  split 
into  forks,  or  lengthen  into  columns,  when  the  proper 
notes  are  sounded. 

Underneath  this  gas-holder  are  placed  two  small  basins, 
18 


272  SOUND. 

the  one  containing  hydrochloric  acid,  and  the  other  am- 
monia. Fumes  of  sal-ammoniac  are  thus  copiously  formed, 
and  mingle  with  the  gas  contained  in  the  holder.  We 
may,  as  already  stated,  operate  with  coal-gas,  carbonic 
acid,  air,  or  hydrogen;  each  of  them  yields  good  effects. 
From  our  excellent  steatite  burner  now  issues  a  thin  col- 
umn of  smoke.  On  sounding  the  whistle,  which  was  so 
effective  with  the  flames,  it  is  found  ineffective.  When, 
moreover,  the  highest  notes  of  Pandean  pipes  are 
sounded,  they  are  also  ineffective.  Kor  will  the  lowest 
notes  answer.  But  when  a  certain  pipe,  which  stands 
about  the  middle  of  the  series,  is  sounded,  the  smoke- 
column  falls,  forming  a  short  stem  with  a  thick,  bushy 
head.  It  is  also  pressed  down,  as  if  by  a  vertical  wind, 
by  a  knock  upon  the  table.  At  every  tap  it  drops.  A 
stroke  on  an  anvil,  on  the  contrary,  produces  little  or  no 
effect.  In  fact,  the  notes  here  effective  are  of  a  much 
lower  pitch  than  those  which  were  most  efficient  in  the 
case  of  the  flames. 

The  amount  of  shrinkage  exhibited  by  some  of  these 
smoke-columns,  in  proportion  to  their  length,  is  far  greater 
than  that  of  the  flames.  A  tap  on  the  table  causes  a 
smoke-jet  eighteen  inches  high  to  shorten  to  a  bushy  bou- 
quet, with  a  stem  not  more  than  an  inch  in  height.  The 
smoke-columns,  in  proportion  to  their  length,  is  far  greater 
knocks  it  down;  and  it  dances  to  the  tune  of  a  musical- 
box.  Some  notes  cause  the  mere  top  of  the  smoke-column 
to  gather  itself  up  into  a  bunch ;  at  other  notes  the  bunch 
is  formed  midway  down;  while  notes  of  more  suitable 
pitch  cause  the  column  to  contract  itself  to  a  cumulus  not 
much  more  than  an  inch  above  the  end  of  the  burner. 
Various  forms  of  the  dancing  smoke-jet  are  shown  in  Fig. 
139.  As  the  music  continues,  the  action  of  the  smoke- 
column  consists  of  a  series  of  rapid  leaps  from  one  of  these 
forms  to  another. 


SENSITIVE  SMOKE-JETS. 


273 


FIG.  139. 


In  a  perfectly  still  atmosphere  these  slender  smoke- 
columns  rise  sometimes  to  a  height  of  nearly  two  feet, 
apparently  vanishing  into  air  at  the  summit.  When  this 
is  the  case,  our  most 
sensitive  flames  fall  far 
behind  them  in  delicacy; 
and  though  less  striking 
than  the  flames,  the 
smoke-wreaths  are  often 
more  graceful.  Not  only 
special  words,  but  every 
word,  and  even  every 
syllable,  of  the  foregoing 
stanza  from  Spenser, 
tumbles  a  really  sensitive 
smoke-jet  into  confusion. 
To  produce  such  effects, 


a  perfectly  tranquil  at- 
mosphere   is    necessary. 
Flame-experiments,  in  fact,  are  possible  in  an  atmosphere 
where  smoke-jets  are  utterly  unmanageable.1 

§15.  Constitution  of  Liquid  Veins:  Sensitive 
Water-jets. 

We  have  thus  far  confined  our  attention  to  jets  of 
ignited  and  unignited  coal-gas — of  carbonic  acid,  hydro- 
gen, and  air.  We  will  now  turn  to  jets  of  water.  And 
here  a  series  of  experiments,  remarkable  for  their 

1  Referring  to  these  effects,  Helmholtz  says :  "  Die  erstannliche  Em- 
pfindlichkeit  eines  init  Rauch  impragnirten  cylindrischen  Luftstrahls 
gegen  Schall  ist  von  Herrn  Tyndall  beschrieben  worden;  ich  habe 
dieselbe  bestStigt  gefunden.  Es  ist  dies  offenbar  eine  Eigenschaft  der 
Trennungsflachen  die  fur  das  Anblasen  der  Pfeifen  von  grosster 
AViohtigkoit  ist." — ("  Discontinuirliche  Luftbewegung,"  Monatsbericht, 
April,  1868.) 


274 


SOUND. 


FIG.  140. 
a 


FIG.  141.  FIG.  142.  beauty,  has  long  existed,  which 
claim  relationship  to  those  just 
described.  These  are  the  ex- 
periments of  Felix  Savart  on 
liquid  veins.  If  the  bottom 
of  a  vessel  containing  water 
be  pierced  by  a  circular  ori- 
fice, the  descending  liquid  vein 
will  exhibit  two  parts  unmis- 
takably distinct.  The  part  o± 
the  vein  nearest  the  orifice  is 
steady  and  limpid,  presenting 
the  appearance  of  a  solid  glass 
rod.  It  decreases  in  diameter 
as  it  descends,  reaches  a  point 
of  maximum  contraction,  from 
which  point  downward  it  ap- 
pears turbid  and  unsteady.  The 
course  of  the  vein,  moreover,  is 
marked  by  periodic  swellings 
and  contractions.  Savart  has 
represented  these  appearances 
as  in  Fig.  140.  The  part  a  n 
nearest  the  orifice  is  limpid 
and  steady,  while  all  the  part 
below  n  is  in  a  state  of  quiver- 
ing motion.  This  lower  part 
of  the  vein  appears  continuous 
to  the  eye;  but  the  finger  can 
be  sometimes  passed  through 
it  without  being  wetted.  This, 
of  course,  could  not  be  the 
case  if  the  vein  were  really 
continuous.  The  upper  por- 
tion of  the  vein,  moreover, 


CONSTITUTION  OF  LIQUID   VEINS.  275 

intercepts  vision;  the  lower  portion,  even  when  the  liquid 
is  mercury,  does  not.  In  fact,  the  vein  resolves  itself,  at 
n,  into  liquid  spherules,  its  apparent  continuity  being  due 
to  the  retention  of  the  impressions  made  by  the  falling 
drops  upon  the  retina.  If,  while  looking  at  the  disturbed 
portion  of  the  vein,  the  head  be  suddenly  lowered,  the 
descending  column  will  be  resolved  for  a  moment  into 
separate  drops.  Perhaps  the  simplest  way  of  reducing 
the  vein  to  its  constituent  spherules  is  to  illuminate  the 
vein,  in  a  dark  room,  by  a  succession  of  electric  flashes. 
Every  flash  reveals  the  drops,  as  if  they  were  perfectly 
motionless  in  the  air. 

Could  the  appearance  of  the  vein  illuminated  by  a 
single  flash  be  rendered  permanent,  it  would  be  that  rep- 
resented in  Fig.  141.  And  here  we  find  revealed  the 
cause  of  those  swellings  and  contractions  which  the  dis- 
turbed portion  of  the  vein  exhibits.  The  drops,  as  they 
descend,  are  continually  changing  their  forms.  When  first 
detached  from  the  end  of  the  limpid  portion  of  the  vein, 
the  drop  is  a  spheroid  with  its  longest  axis  vertical.  But 
a  liquid  cannot  retain  this  shape,  if  abandoned  to  the 
forces  of  its  own  molecules.  The  spheroid  seeks  to  become 
a  sphere — the  longer  diameter,  therefore,  shortens;  but, 
like  a  pendulum  which  seeks  to  return  to  its  position  of 
rest,  the  contraction  of  the  vertical  diameter  goes  too  far, 
and  the  drop  becomes  a  flattened  spheroid.  Now,  the 
contractions  of  the  jet  are  formed  at  those  places  where 
the  longest  axis  of  the  drop  is  vertical,  while  the  swellings 
appear  where  the  longest  axis  is  horizontal.  It  will  be 
noticed  that  between  every  two  of  the  larger  drops  is  a 
third  one  of  much  smaller  dimensions.  According  to 
Savart,  their  appearance  is  invariable. 

I  wish  to  make  the  constitution  of  a  liquid  vein  evi- 
dent to  you  by  a  simple  but  beautiful  experiment.  The 
condensing  lens  has  been  removed  from  our  electric  lamp, 


276  SOUND. 

the  light  being  permitted  to  pass  through  a  vertical  slit 
directly  from  the  carbon-points.  The  slice  of  light  thus 
obtained  is  so  divergent  that  it  illuminates,  from  top  to 
bottom,  a  liquid  vein  several  feet  long,  and  placed  at  some 
distance  from  the  lamp.  Immediately  in  front  of  the 
camera  is  a  large  disk  of  zinc  with  six  radial  slits,  about 
ten  inches  long  and  an  inch  wide.  By  the  rotation  of  the 
disk  the  light  is  caused  to  fall  in  flashes  upon  the  jet;  and, 
when  the  suitable  speed  of  rotation  has  been  attained,  the 
vein  is  resolved  into  its  constituent  spherules.  Keceiving 
the  shadow  of  the  vein  upon  a  white  screen,  its  constitu- 
tion is  rendered  clearly  visible  to  all  here  present. 

This  breaking-up  of  a  liquid  vein  into  drops  has  been 
a  subject  of  frequent  experiment  and  much  discussion. 
Savart  traced  the  pulsations  to  the  orifice,  but  he  did  not 
think  that  they  were  produced  by  friction.  They  are 
powerfully  influenced  by  sonorous  vibrations.  In  the 
midst  of  a  large  city  it  is  hardly  possible  to  obtain  the 
requisite  tranquillity  for  the  full  development  of  the  con- 
tinuous portion  of  the  vein;  still,  Savart  was  so  far  able 
to  withdraw  his  vein  from  the  influence  of  such  irregular 
vibrations,  that  its  limpid  portion  became  elongated  to 
the  extent  shown  in  Fig.  142.  It  will  be  understood  that 
Fig.  141  represents  a  vein  exposed  to  the  irregular  vibra- 
tions of  the  city  of  Paris,  while  Fig.  142  represents  one 
produced  under  precisely  the  same  conditions,  but  with- 
drawn from  those  vibrations. 

The  drops  into  which  the  vein  finally  resolves  itself 
are  incipient  even  in  its  limpid  portion,  announcing 
themselves  there  as  annular  protuberances,  which  become 
more  and  more  pronounced,until  finally  they  separate. 
Their  birthplace  is  near  the  orifice  itself,  and  under  even 
moderate  pressure  they  succeed  each  other  with  sufficient 
rapidity  to  produce  a  feeble  musical  note.  By  permitting 


ANALYSIS  OF  LIQUID  VEINS.  277 

the  drops  to  fall  upon  a  membrane,  the  pitch  of  this  note 
may  be  fixed;  and  now  we  come  to  the  point  which  con- 
nects the  phenomena  of  liquid  veins  with  those  of  sensi- 
tive flames  and  smoke-jets.  If  a  note  in  unison  with  that 
of  the  vein  be  sounded  near  it,  the  limpid  portion  in- 
stantly shortens;  the  pitch  may  vary  to  some  extent,  and 
still  cause  a  shortening;  but  the  unisonant  note  is  the 
most  effectual.  Savart's  experiments  on  vertically-de- 
scending veins  have  been  recently  repeated  in  our  labora- 
tory with  striking  effect.  From  a  distance  of  thirty  yards 
the  limpid  portion  of  the  vein  has  been  shortened  by  the 
sound  of  an  organ-pipe  of  the  proper  pitch  and  of  moder- 
ate intensity. 

I  have  also  recently  gone  carefully,  not  merely  by 
reading,  but  by  experiment,  over  Plateau's  account  of  the 
resolution  of  a  liquid  vein  into  drops.  In  his  researches 
on  the  figures  of  equilibrium  of  bodies  withdrawn  from 
the  action  of  gravity,  he  finds  that  a  liquid  cylinder  is 
stable  as  long  as  its  length  does  not  exceed  three  times  its 
diameter;  or,  more  accurately,  as  long  as  the  ratio  be- 
tween them  does  not  exceed  that  of  the  diameter  of  a  cir- 
cle to  its  circumference,  or  3,1416.  If  this  be  a  little  ex- 
ceeded the  cylinder  begins  to  narrow  at  some  point  or 
other  of  its  length;  nips  itself  together,  breaks,  and  forms 
immediately  two  spheres.  If  the  ratio  of  the  length  of 
the  cylinder  to  its  diameter  greatly  exceed  3,1416,  then, 
instead  of  breaking  up  into  two  spheres,  it  breaks  up  into 
several. 

A  liquid  cylinder  may  be  obtained  by  introducing 
olive-oil  into  a  mixture  of  alcohol  and  water,  of  the  same 
density  as  the  oil.  The  latter  forms  a  sphere.  Two  disks 
of  smaller  diameter  than  the  sphere  are  brought  into 
contact  with  it,  and  then  drawn  apart;  the  oil  clings  to 
the  disks,  and  the  sphere  is  transformed  into  a  cylinder. 


278  SOUND. 

If  the  quantity  of  oil  be  insufficient  to  produce  the  maxi- 
mum length  of  the  cylinder,  more  may  be  added  by  a 
pipette.  In  making  this  experiment  it  will  be  noticed 
that,  when  the  proper  length  is  exceeded,  the  nipped  por- 
tion of  the  cylinder  elongates,  and  exists  for  a  moment  as 
a  very  thin  liquid  cylinder  uniting  the  two  incipient 
spheres;  and  that,  when  rupture  occurs,  the  thin  cylinder, 
which  has  also  exceeded  its  proper  length,  breaks  so  as  to 
form  a  small  spherule  between  the  two  larger  ones.  This 
is  a  point  of  considerable  significance  in  relation  to  our 
present  question. 

Now,  Plateau  contends  that  the  play  of  the  molecular 
forces  in  a  liquid  cylinder  is  not  suspended  by  its  motion 
of  translation.  The  first  portion  of  a  vein  of  water  quit- 
ting an  orifice  is  a  cylinder,  to  which  the  laws  which  he 
has  established  regarding  motionless  cylinders  apply.  The 
moment  the  descending  vein  exceeds  the  proper  length  it 
begins  to  pinch  itself  so  as  to  form  drops;  but  urged  for- 
ward as  it  is  by  the  pressure  above  it,  and  by  its  own 
gravity,  in  the  time  required  for  the  rounding  of  the  drop 
it  reaches  a  certain  distance  from  the  orifice.  At  this 
distance,  the  pressure  remaining  constant,  and  the  vein 
being  withdrawn  from  external  disturbance,  rupture  inva- 
riably occurs.  And  the  rupture  is  accompanied  by  the 
phenomenon  which  has  just  been  called  significant.  Be- 
tween every  two  succeeding  large  drops  a  small  spherule 
is  formed,  as  shown  in  Fig.  141. 

Permitting  a  vein  of  oil  to  fall  from  an  orifice,  not 
through  the  air,  but  through  a  mixture  of  alcohol  and 
water  of  the  proper  density,  the  continuous  portion  of  the 
vein,  its  resolution  into  drops,  and  the  formation  of  the 
small  spherule  between  each  liberated  drop  and  the  end 
of  the  liquid  cylinder  which  it  has  just  quitted,  may  be 
watched  with  the  utmost  deliberation.  The  effect  of  this 


ACTION  OF  SOUND  ON  VERTICAL  JETS.  279 

and  other  experiments  upon  the  mind  will  be  to  produce 
the  conviction  that  the  very  beautiful  explanation  offered 
by  Plateau  is  also  the  true  one.  The  various  laws  estab- 
lished experimentally  by  Savart  all  follow  immediately 
from  Plateau's  theory. 

In  a  small  paper  published  more  than  twenty  years 
ago  I  drew  attention  to  the  fact  that  when  a  descending 
vein  intersects  a  liquid  surface  above  the  point  of  rup- 
ture, if  the  pressure  be  not  too  great,  it  enters  the  liquid 
silently;  but  when  the  surface  intersects  the  vein  below 
the  point  of  rupture  a  rattle  is  immediately  heard,  and 
bubbles  are  copiously  produced.  In  the  former  case,  not 
only  is  there  no  violent  dashing  aside  of  the  liquid,  but 
round  the  base  of  the  vein,  and  in  opposition  to  its  motion, 
the  liquid  collects  in  a  heap,  by  its  surface  tension  or  capil- 
lary attraction.  This  experiment  can  be  combined  with 
two  other  observations  of  Savart's,  in  a  beautiful  and  in- 
structive manner.  In  addition  to  the  shortening  of  the 
continuous  portion  by  sound,  Savart  found  that,  when  he 
permitted  his  membrane  to  intersect  the  vein  at  one  of  its 
protuberances,  the  sound  was  louder  than  when  the  inter- 
section occurred  at  the  contracted  portion. 

I  permitted  a  vein  to  descend,  under  scarcely  any 
pressure,  from  a  tube  three-quarters  of  an  inch  in  diam- 
eter, and  to  enter  silently  a  basin  of  water  placed  nearly 
20  inches  below  the  orifice.  On  sounding  vigorously  a 
TJt2  tuning-fork  the  pellucid  jet  was  instantly  broken, 
and  as  many  as  three  of  its  swellings  were  seen  above  the 
surface.  The  rattle  of  air-bubbles  was  instantly  heard, 
and  the  basin  was  seen  to  be  filled  with  them.  The  sound 
was  allowed  slowly  to  die  out;  the  continuous  portion  of 
the  vein  lengthened,  and  a  series  of  alternations  in  the 
production  of  the  bubbles  was  observed.  When  the  swell- 
ings of  the  vein  cut  the  surface  of  the  water,  the  bubbles 


2SO  SOUND. 

were  copious  and  loud;  when  the  contracted  portions 
crossed  the  surface,  the  bubbles  were  scanty  and  scarcely 
audible. 

Removing  the  basin,  placing  an  iron  tray  in  its  place, 
and  exciting  the  fork,  the  vein,  which  at  first  struck 
silently  upon  the  tray,  commenced  a  rattle  which  rose  and 
sank  with  the  dying  out  of  the  sound,  according  as  the 
swellings  or  contractions  of  the  jet  impinged  upon  the 
surface.  This  is  a  simple  and  beautiful  experiment. 

Savart  also  caused  his  vein  to  issue  horizontally  and 
at  various  inclinations  to  the  horizon,  and  found  that,  in 
certain  cases,  sonorous  vibrations  were  competent  to  cause 
a  jet  to  divide  into  two  or  three  branches.  In  these  ex- 
periments the  liquid  was  permitted  to  issue  through  an 
orifice  in  a  thin  plate.  Instead  of  this,  however,  we  will 
resort  to  our  favorite  steatite  burner;  for  with  water 
also  it  asserts  the  same  mastery  over  its  fellows  that  it 
exhibited  with  flames  and  smoke- jets.  It  will,  moreover, 
reveal  to  us  some  entirely  novel  results.  By  means  of  an 
India-rubber  tube  the  burner  is  connected  with  the  water- 
pipes  of  the  Institution,  and,  by  pointing  it  obliquely 
upward,  we  obtain  a  fine  parabolic  jet  (Fig.  143).  At  a 
certain  distance  from  the  orifice,  the  vein  resolves  itself 
into  beautiful  spherules,  whose  motions  are  not  rapid 
enough  to  make  the  vein  appear  continuous.  At  the 
vertex  of  the  parabola  the  spray  of  pearls  is  more  than  an 
inch  in  width,  and,  farther  on,  the  drops  are  still  more 
widely  scattered.  On  sweeping  a  fiddle-bow  across  a 
tuning-fork  which  executes  512  vibrations  in  a  second, 
the  scattered  drops,  as  if  drawn  together  by  their  mutual 
attractions,  instantly  close  up,  and  form  an  apparently 
continuous  liquid  arch  several  feet  in  height  and  span 
(shown  in  Fig.  144).  As  long  as  the  proper  note  is  main- 
tained the  vein  looks  like  a  frozen  band,  so  motionless 


ACTION  OF  SOUND  ON  OBLIQUE  JETS.  281 

does  it  appear.  On  stopping  the  fork  the  arch  is  shaken 
asunder,  and  we  have  the  same  play  of  liquid  pearls  as 
before.  Every  sweep  of  the  bow,  however,  causes  the 
drops  to  fall  into  a  common  line  of  march. 

A  pitch-pipe,  or  an  organ-pipe  yielding  the  note  of 

FIG.  143. 


145. 


this  tuning-fork,  also  powerfully  controls  the  vein.  The 
voice  does  the  same.  On  pitching  it  to  a  note  of  moder- 
ate intensity,  it  causes  the  wandering  drops  to  gather' 
themselves  together.  At  a  distance  of  twenty  yards,  the 
voice  is,  to  all  appearance,  as  powerful  in  curbing  the 


282  SOUND. 

vein,  and  causing  its  drops  to  close  up,  as  it  is  when  close 
to  the  issuing  jet. 

The  effect  of  "  beats  "  upon  the  vein  is  also  beautiful 
and  instructive.  They  may  be  produced  either  by  organ- 
pipes  or  by  tuning-forks.  When  two  forks  vibrate,  the 
one  512  times  and  the  other  508  times  in  a  second,  you 
will  learn  in  our  next  lecture  that  they  produce  four  beats 
in  a  second.  When  the  forks  are  sounded  the  beats  are 
heard,  and  the  liquid  vein  is  seen  to  gather  up  its  pearls, 
and  scatter  them  in  synchronism  with  the  beats.  The 
sensitiveness  of  this  vein  is  astounding;  it  rivals  that  of 
the  ear  itself.  Placing  the  two  tuning-forks  on  a  distant 
table,  and  permitting  the  beats  to  die  gradually  out,  the 
vein  continues  its  rhythm  almost  as  long  as  hearing  is 
possible.  A  more  sensitive  vein  might  actually  prove 
superior  to  the  ear — a  very  surprising  result,  considering 
the  marvelous  delicacy  of  this  organ.1 

By  introducing  a  Leyden-jar  into  the  circuit  of  a 
powerful  induction-coil,  a  series  of  dense  and  dazzling 
flashes  of  light,  each  of  momentary  duration,  is  obtained. 
Every  such  flash  in  a  darkened  room  renders  the  drops 
distinct,  each  drop  being  transformed  into  a  little  star  of 
intense  brilliancy.  If  the  vein  be  then  acted  on  by  a 
sound  of  the  proper  pitch,  it  instantly  gathers  its  drops 
together  into  a  necklace  of  inimitable  beauty. 

In  these  experiments  the  whole  vein  gathers  itself  into 
a  single  arched  band  when  the  proper  note  is  sounded; 
but,  by  varying  the  conditions,  it  may  be  caused  to  divide 
into  two  or  more  such  bands,  as  shown  in  Fig.  145.  Draw- 
ings, however,  are  ineffectual  here;  for  the  wonder  of 
these  experiments  depends  mainly  on  the  sudden  transi- 
tion of  the  vein  from  one  state  to  the  other.  In  the 

1  When  these  two  tuning-forks  were  placed  in  contact  with  a  vessel 
from  which  a  liquid  vein  issued,  the  visible  action  on  the  vein  con- 
tinued long  after  the  forks  had  ceased  to  be  heard. 


ACTION  OF  SOUND  ON  OBLIQUE  JETS.  283 

motion  dwells   the   surprise,   and  this   no   drawing   can 
render.1 

1  The  experiments  on  sounding  flames  have  been  recently  consider- 
ably extended  by  my  assistant  Mr.  Cottrell.  By  causing  flame  to  rub 
against  flame,  various  musical  sounds  can  be  obtained — some  resem- 
bling those  of  a  trumpet,  others  those  of  a  lark.  By  the  friction  of 
unignited  gas-jets,  similar  though  less  intense  effects  are  produced. 
When  the  two  flames  of  a  fish-tail  burner  are  permitted  to  impinge 
upon  a  plate  of  platinum,  as  in  Scholl's  "  perfectors,"  the  sounds  are 
trumpet-like,  and  very  loud.  Two  ignited  gas-jets  may  be  caused  to 
flatten  out  like  Savart's  water-jets.  Or  they  may  be  caused  to  roll 
themselves  into  two  hollow  horns,  forming  a  most  instructive  example 
of  the  Wirbelflachen  of  Helmholtz.  The  carbon-particles  liberated  in 
the  flame  rise  through  the  horns  in  continuous  red-hot  or  white-hot 
spirals,  which  are  extinguished  at  a  height  of  some  inches  from  their 
place  of  generation. 


284  SOUND. 


SUMMARY  OF  CHAPTER  VI. 

WHEN  a  gas-flame  is  placed  in  a  tube,  the  air  in  pass- 
ing over  the  flame  is  thrown  into  vibration,  musical 
sounds  being  the  consequence. 

Making  allowance  for  the  high  temperature  of  the 
column  of  air  associated  with  the  flame,  the  pitch  of  the 
note  is  that  of  an  open  organ-pipe  of  the  length  of  the  tube 
surrounding  the  flame. 

The  vibrations  of  the  flame,  while  the  sound  contin- 
ues, consist  of  a  series  of  periodic  extinctions,  total  or  par- 
tial, between  every  two  of  which  the  flame  partially  recov- 
ers its  brightness. 

The  periodicity  of  the  phenomenon  may  be  demon- 
strated by  means  of  a  concave  mirror  which  forms  an 
image  of  the  vibrating  flame  upon  a  screen.  When  the 
image  is  sharply  defined,  the  rotation  of  the  mirror  reduces 
the  single  image  to  a  series  of  separate  images  of  the  flame. 
The  dark  spaces  between  the  images  correspond  to  the  ex- 
tinctions of  the  flame,  while  the  images  themselves  corre- 
spond to  its  periods  of  recovery. 

Besides  the  fundamental  note  of  the  associated  tube, 
the  flame  can  also  be  caused  to  excite  the  higher  overtones 
of  the  tube.  The  successive  divisions  of  the  column  of  air 
are  those  of  an  open  organ-pipe  when  its  harmonic  tones 
are  sounded. 

On  sounding  a  note  nearly  in  unison  with  a  tube  con- 
taining a  silent  flame,  the  flame  jumps;  and  if  the  position 
of  the  flame  in  the  tube  be  rightly  chosen,  the  extraneous 
sound  will  cause  the  flame  to  sing. 


SUMMARY.  285 

While  the  flame  is  singing,  a  note  nearly  in  unison 
with  its  own  produces  beats,  and  the  flame  is  seen  to  jump 
in  synchronism  with  the  beats.  The  jumping  is  also  ob- 
served when  the  position  of  the  flame  within  its  tube  is 
not  such  as  to  enable  it  to  sing. 


NAKED    FLAMES. 

When  the  pressure  of  the  gas  which  feeds  a  naked 
flame  is  augmented,  the  flame,  up  to  a  certain  point,  in- 
creases in  size.  But  if  the  pressure  be  too  great,  the  flame 
roars  or  flares. 

The  roaring  or  flaring  of  the  flame  is  caused  by  the 
state  of  vibration  into  which  the  gas  is  thrown  in  the  ori- 
fice of  the  burner,  when  the  pressure  which  urges  it 
through  the  orifice  is  excessive. 

•If  the  vibrations  in  the  orifice  of  the  burner  be  super- 
induced by  an  extraneous  sound,  the  flame  will  flare  under 
a  pressure  less  than  that  which,  of  itself,  would  produce 
flaring. 

The  gas  under  excessive  pressure  has  vibrations  of  a 
definite  period  impressed  upon  it  as  it  passes  through  the 
burner.  To  operate  with  a  maximum  effect  upon  the 
flame  the  external  sound  must  contain  vibrations  synchro- 
nous with  those  of  the  issuing  gas. 

When  such  a  sound  is  chosen,  and  when  the  flame  is 
brought  sufficiently  near  its  flaring-point,  it  furnishes  an 
acoustic  reagent  of  unexampled  delicacy. 

At  a  distance  of  30  yards,  for  example,  the  chirrup  of 
a  house-sparrow  would  be  competent  to  throw  the  flame 
into  commotion. 

It  is  not  to  the  flame,  as  such,  that  we  are  to  ascribe 
these  effects.  Effects  substantially  similar  are  produced 
when  we  employ  jets  of  unignited  coal-gas,  carbonic  acid, 
hydrogen,  or  air.  These  jets  may  be  rendered  visible  by 


286  ,  SOUND. 

smoke,  and  the  smoke-jets  show  a  sensitiveness  to  sonorous 
vibrations  even  greater  than  that  of  the  flames. 

When  a  brilliant  sensitive  flame  illuminates  an  other- 
wise dark  room,  in  which  a  suitable  bell  is  caused  to  strike, 
a  series  of  periodic  quenchings  of  the  light  by  the  sound 
occurs.  Every  stroke  of  the  bell  is  accompanied  by  a  mo- 
mentary darkening  of  the  room. 

A  jet  of  water  descending  from  a  circular  orifice  is 
composed  of  two  distinct  portions,  the  one  pellucid  and 
calm;  the  other  in  commotion.  "When  properly  analyzed 
the  former  portion  is  found  continuous;  the  latter  being 
a  succession  of  drops. 

If  these  drops  be  received  upon  a  membrane,  a  musical 
sound  is  produced.  When  an  extraneous  sound  of  this 
particular  pitch  is  produced  in  the  neighborhood  of  the 
vein,  the  continuous  portion  is  seen  to  shorten. 

The  continuous  portion  of  the  vein  presents  a  series  of 
swellings  and  contractions,  in  the  former  of  which  the 
drops  are  flattened,  and  in  the  latter  elongated.  The 
sound  produced  by  the  flattened  drops  on  striking  the 
membrane  is  louder  than  that  produced  by  the  elongated 
ones. 

Above  its  point  of  rupture  a  vein  of  water  may  be 
caused  to  enter  water  silently;  but  on  sounding  a  suitable 
note,  the  rattle  of  bubbles  is  immediately  heard;  the  dis- 
continuous part  of  the  vein  rises  above  the  surface,  and  as 
the  sound  dies  out  the  successive  swellings  and  contrac- 
tions produce  alternations  of  the  quantity  and  sound  of 
the  bubbles. 

In  veins  propelled  obliquely,  the  scattered  water-drops 
may  be  called  together  by  a  suitable  sound,  so  as  to  form 
an  apparently  continuous  liquid  arch. 

Liquid  veins  may  be  analyzed  by  the  electric  spark,  or 
by  a  succession  of  flashes  illuminating  the  veins. 


CHAPTEK  VII. 

RESEARCHES  ON  THE  ACOUSTIC  TRANSPARENCY  OF  THE  AT- 
MOSPHERE IN  RELATION  TO  THE  QUESTION  OF  FOG-SIG- 
NALING. 


PART  I. 

Introduction.— Instruments  and  Observations.— Contradictory  Results 
from  the  19th  of  May  to  the  1st  of  July  inclusive. — Solution  of 
Contradictions. — Aerial  Reflection  and  its  Causes. — Aerial  Echoes. 
—Acoustic  Clouds.— Experimental  Demonstration  of  Stoppage  of 
Sound  by  Aerial  Reflection. 

§  1.  Introduction. 

WE  are  now  fully  equipped  for  the  investigation  of  an 
important  practical  problem.  The  cloud  produced  by  the 
puff  of  a  locomotive  can  quench  the  rays  of  the  noonday 
sun;  it  is  not,  therefore,  surprising  that  in  dense  fogs  our 
most  powerful  coast-lights,  including  even  the  electric 
light,  should  become  useless  to  the  mariner. 

Disastrous  shipwrecks  are  the  consequence.  During 
the  last  ten  years  no  less  than  two  hundred  and  seventy- 
three  vessels  have  been  reported  as  totally  lost  on  our  own 
coasts  in  fog  or  thick  weather.  The  loss,  I  believe,  has 
been  far  greater  on  the  American  seaboard,  where  trade  is 
more  eager,  and  fogs  more  frequent,  than  they  are  here. 
No  wonder,  then,  that  earnest  efforts  should  be  made  to 
find  a  substitute  for  light  in  sound-signals,  powerful 
enough  to  give  warning  and  guidance  to  mariners  while 
still  at  a  safe  distance  from  the  shore. 
19  287 


288  SOUND. 

Such  signals  have  been  established  to  some  extent  upon 
our  own  coasts,  and  to  a  still  greater  extent  along  the 
coasts  of  Canada  and  the  United  States.  But  the  evidence 
as  to  their  value  and  performance  is  of  the  most  conflicting 
character,  and  no  investigation  sufficiently  thorough  to 
clear  up  the  uncertainty  has  hitherto  been  made.  In  fact, 
while  the  velocity  of  sound  has  formed  the  subject  of  re- 
fined and  repeated  experiment  by  the  ablest  philosophers, 
the  publication  of  Dr.  Derham's  celebrated  paper  in  the 
"  Philosophical  Transactions  "  for  1708  marks  the  latest 
systematic  inquiry  into  the  causes  which  affect  the  inten- 
sity of  sound  in  the  atmosphere. 

Jointly  with  the  Elder  Brethren  of  the  Trinity  House, 
and  as  their  scientific  adviser,  I  have  recently  had  the 
honor  of  conducting  an  inquiry  designed  to  fill  the  blank 
here  indicated. 

One  or  two  brief  references  will  suffice  to  show  the 
state  of  the  question  when  this  investigation  began. 
"  Derham,"  says  Sir  John  Herschel,  "  found  that  fogs 
and  falling  rain,  but  more  especially  snow,  tend  power- 
fully to  obstruct  the  propagation  of  sound,  and  that  the 
same  effect  was  produced  by  a  coating  of  fresh-fallen  snow 
on  the  ground,  though  when  glazed  and  hardened  at  the 
surface  by  freezing  it  had  no  such  influence."  * 

In  a  very  clear  and  able  letter,  addressed  to  the  Presi- 
dent of  the  Board  of  Trade  in  1863,2  Dr.  Robinson,  of 
Armagh,  thus  summarizes  our  knowledge  of  fog-signals: 
"  Nearly  all  that  is  known  about  fog-signals  is  to  be  found 
in  the  '  Report  on  Lights  and  Beacons;'  and  of  it  much  is 
little  better  than  conjecture.  Its  substance  is  as  follows: 

"  '  Light  is  scarcely  available  for  this  purpose.  Blue 
lights  are  used  in  the  Hooghly;  but  it  is  not  stated  at 
what  distance  they  are  visible  in  fog;  their  glare  may  be 

1  "Essay  on  Round."  par.  21. 

*  "  Report  of  the  British  Association  for  1863,"  p.  105. 


SUMMARY  OF  EXISTING  KNOWLEDGE.  289 

seen  farther  than  their  flame.1  It  might,  however,  be 
desirable  to  ascertain  how  far  the  electric  light,  or  its 
flash,  can  be  traced.2 

"  '  Sound  is  the  only  known  means  really  effective; 
but  about  it  testimonies  are  conflicting,  and  there  ia 
scarcely  one  fact  relating  to  its  use  as  a  signal  which  can 
be  considered  as  established.  Even  the  most  important  of 
all,  the  distance  at  which  it  ceases  to  be  heard,  is  unde- 
cided. 

"  '  Up  to  the  present  time  all  signal-sounds  have  been 
made  in  air,  though  this  medium  has  grave  disadvantages: 
its  own  currents  interfere  with  the  sound-waves,  so  that  a 
gun  or  bell  which  is  heard  several  miles  down  the  wind  is 
inaudible  more  than  a  few  furlongs  up  it.  A  still  greater 
evil  is  that  it  is  least  effective  when  most  needed;  for  fog 
is  a  powerful  damper  of  sound.'  " 

Dr.  Robinson  here  expresses  the  universally-prevalent 
opinion,  and  he  then  assigns  the  theoretic  cause.  "  Fog," 
he  says,  "  is  a  mixture  of  air  and  globules  of  water,  and  at 
each  of  the  innumerable  surfaces  where  these  two  touch, 
a  portion  of  the  vibration  is  reflected  and  lost.3  .  .  . 
Snow  produces  a  similar  effect,  and  one  still  more  inju- 
rious." 

Reflection  being  thus  considered  to  take  place  at  the 
surfaces  of  the  suspended  particles,  it  followed  that  the 
greater  the  number  of  particles,  or,  in  other  words,  the 
denser  the  fog,  the  more  injurious  would  be  its  action 
upon  sound.  Hence  optic  transparency  came  to  be  con- 
sidered a  measure  of  acoustic  transparency.  On  this 
point  Dr.  Robinson,  in  the  letter  referred  to,  expresses 
himself  thus:  "  At  the  outset,  it  is  obvious  that,  to  make 

1  A  very  sagacious  remark,  as  observation  proves. 

2  Powerful  electric  lights  have  since  been  established  and  found 
ineffectual. 

8  This  is  also  Sir  John  Herschel's  way  of  regarding  the  subject. 
•'  Essay  on  Sound,"  par.  38. 


290  SOUND. 

experiments  comparable,  we  must  have  some  measure  of 
the  fog's  power  of  stopping  sound,  without  attending  to 
which  the  most  anomalous  results  may  be  expected.  It 
seems  probable  that  this  will  bear  some  simple  relation  to 
its  opacity  to  light,  and  that  the  distance  at  which  a  given 
object,  as  a  flag  or  pole,  disappears  may  be  taken  as  the 
measure."  "  Still,  clear  air  "  was  regarded  in  this  letter 
as  the  best  vehicle  of  sound,  the  alleged  action  of  fogs, 
rain,  and  snow,  being  ascribed  to  their  rendering  the  at- 
mosphere "  a  discontinuous  medium." 

Prior  to  the  investigation  now  to  be  described  the  views 
here  enunciated  were  those  universally  entertained.  That 
sound  is  unable  to  penetrate  fogs  was  taken  to  be  "a  matter 
of  common  observation."  The  bells  and  horns  of  ships 
were  affirmed  "  not  to  be  heard  so  far  in  fogs  as  in  clear 
weather."  In  the  fogs  of  London  the  noise  of  the  car- 
riage-wheels was  reported  to  be  so  much  diminished  that 
"  they  seem  to  be  at  a  distance  where  really  close  by." 
My  knowledge  does  not  inform  me  of  the  existence  of  any 
other  source  for  these  opinions  regarding  the  deadening 
power  of  fog  than  the  paper  of  Derham,  published  one 
hundred  and  sixty-seven  years  ago.  In  consequence  of 
their  a  priori  probability,  his  conclusions  seem  to  have 
been  transmitted  unquestioned  from  generation  to  genera- 
tion of  scientific  men. 

§  2.  Instruments  and  Observations. 

On  the  19th  of  May,  1873,  this  inquiry  began.  The 
South  Foreland,  near  Dover,  was  chosen  as  the  signal- 
station,  steam-power  having  been  already  established 
there  to  work  two  powerful  magneto-electric  lights.  The 
observations  for  the  most  part  were  made  afloat,  one  of 
the  yachts  of  the  Trinity  Corporation  being  usually  em- 
ployed for  this  purpose.  Two  stations  had  been  established, 
the  one  at  the  top,  the  other  at  the  bottom,  of  the  South 


FOG-SIGNAL  STATION  AT  SOUTH  FORELAND.       291 

Foreland  Cliff;  and  at  each  of  them  trumpets,  air-whistles, 
and  steam-whistles  of  great  size,  were  mounted.  The 
whistles  first  employed  were  of  English  manufacture.  To 
these  was  afterward  added  a  large  United  States  whistle, 
and  also  a  Canadian  whistle,  of  great  reputed  power. 

On  the  8th  of  October  another  instrument,  which  has 
played  a  specially  important  part  in  these  observations, 
was  introduced.  This  was  a  steam-siren,  constructed 
and  patented  by  Mr.  Brown,  of  New  York,  and  intro- 
duced by  Prof.  Henry  into  the  lighthouse  system  of  the 
United  States.  As  an  example  of  international  cour- 
tesy worthy  of  imitation,  I  refer  with  pleasure  to  the  fact 
that  when  informed  by  Major  Elliott,  of  the  United  States 
Army,  that  our  experiments  had  begun,  the  Lighthouse 
Board  at  Washington,  of  their  own  spontaneous  kindness, 
forwarded  to  us  for  trial  a  very  noble  instrument  of  this 
description,  which  was  immediately  mounted  at  the  South 
Foreland. 

In  the  steam-siren,  as  in  the  ordinary  one,  described 
in  Chapter  II.,  a  fixed  disk  and  a  rotating  disk  are  em- 
ployed, but  radial  slits  are  used  instead  of  circular  aper- 
tures. One  disk  is  fixed  vertically  across  the  throat  of  a 
conical  trumpet  16^  feet  long,  5  inches  in  diameter  where 
the  disk  crosses  it,  and  gradually  opening  out  till  at  the 
other  extremity  it  reaches  a  diameter  of  2  feet  3  inches. 
Behind  the  fixed  disk  is  the  rotating  one,  which  is  driven 
by  separate  mechanism.  The  trumpet  is  connected  with 
a  boiler.  In  our  experiments  steam  of  70  Ibs.  pressure 
was  for  the  most  part  employed.  Just  as  in  the  ordinary 
siren,  when  the  radial  slits  of  the  two  disks  coincide,  and 
then  only,  a  strong  puff  of  steam  escapes.  Sound-waves 
of  great  intensity  are  thus  sent  through  the  air,  the 
pitch  of  the  note  depending  on  the  velocity  of  rotation. 
(A  drawing  of  the  steam-siren  constitutes  our  frontis- 
piece.) 


292  SOUND. 

To  the  siren,  trumpets,  and  whistles  were  added  three 
guns — an  18-pounder,  a  5^-inch  howitzer,  and  a  13-inch 
mortar.  In  our  summer  experiments  all  three  were  fired; 
but  the  howitzer  having  shown  itself  superior  to  the  other 
guns  it  was  chosen  in  our  autumn  experiments  as  not  only 
a  fair  but  a  favorable  representative  of  this  form  of  sig- 
nal. The  charges  fired  were  for  the  most  part  those  now 
employed  at  Holyhead,  Lundy  Island,  and  the  Kish  light- 
vessel — namely,  3  Ibs.  of  powder.  Gongs  and  bells  were 
not  included  in  this  inquiry,  because  previous  observa- 
tions had  clearly  proved  their  inferiority  to  the  trumpets 
and  whistles. 

On  the  19th  of  May  the  instruments  tested  were: 

On  the  top  of  the  cliff: 

a.  Two  brass  trumpets  or  horns,  11  feet  2  inches  long, 
2  inches  in  diameter  at  the  mouth-piece,  and  opening  out 
at  the  other  end  to  a  diameter  of  22£  inches.  They  were 
provided  with  vibrating  steel  reeds  9  inches  long,  2  inches 
wide,  and  £  inch  thick,  and  were  sounded  by  air  of  18  Ibs. 
pressure. 

&.  A  whistle,  shaped  like  that  of  a  locomotive,  6  inches 
in  diameter,  also  sounded  by  air  of  18  Ibs.  pressure. 

c.  A  steam-whistle,  12  inches  in  diameter,  attached  to 
a  boiler,  and  sounded  by  steam  of  64  Ibs.  pressure. 

At  the  bottom  of  the  cliff: 

d.  Two  trumpets  or  horns,  of  the  same  size  and  ar- 
rangement as  those  above,  and  sounded  by  air  of  the  same 
pressure.     They  were  mounted  vertically  on  the  reservoir 
of  compressed  air;  but  within  about  two  feet  of  their  ex- 
tremities they  were  bent  at  a  right  angle,  so  as  to  present 
their  mouths  to  the  sea. 

e.  A  6-inch  air-whistle,  similar  to  the  one  above,  and 
sounded  by  the  same  means. 

The  upper  instruments  were  235  feet  above  high- 
water  mark,  the  lower  ones  40  feet.  A  vertical  distance 


INSTRUMENTS.  293 

of  195  feet,  therefore,  separated  the  instruments.  A  shaft, 
provided  with  a  series  of  twelve  ladders,  led  from  the  one 
to  the  other. 

Numerous  comparative  experiments  made  at  the  outset 
gave  a  slight  advantage  to  the  upper  instruments.  They, 
therefore,  were  for  the  most  part  employed  throughout  the 
subsequent  inquiry. 

Our  first  observations  were  a  preliminary  discipline 
rather  than  an  organized  effort  at  discovery.  On  May 
19th  the  maximum  distance  reached  by  the  sound  was 
about  three  and  a  half  miles.1  The  wind,  however,  was 
high  and  the  sea  rough,  so  that  local  noises  interfered  to 
some  extent  with  our  appreciation  of  the  sound. 

Mariners  express  the  strength  of  the  wind  by  a  series 
of  numbers  extending  from  0  =  calm  to  12  =  a  hurri- 
cane, a  little  practice  in  common  producing  a  remarkable 
unanimity  between  different  observers  as  regards  the  force 
of  the  wind.  Its  force  on  May  19th  was  6,  and  it  blew 
at  right  angles  to  the  direction  of  the  sound. 

The  same  instruments  on  May  20th  covered  a  greater 
range  of  sound;  but  not  much  greater,  though  the  dis- 
turbance due  to  local  noises  was  absent.  At  4  miles' 
distance  in  the  axes  of  the  horns  they  were  barely  heard, 
the  air  at  the  time  being  calm,  the  sea  smooth,  and 
all  other  circumstances  exactly  those  which  have  been 
hitherto  regarded  as  most  favorable  to  the  transmission 
of  sound.  We  crept  a  little  farther  away,  and  by  stretched 
attention  managed  to  hear  at  intervals,  at  a  distance  of  6 
miles,  the  faintest  hum  of  the  horns.  A  little  farther  out 
we  again  halted;  but  though  local  noises  were  absent,  and 
though  we  listened  intently,  we  heard  nothing. 

This  position,  clearly  beyond  the  range  of  whistles  and 
trumpets,  was  expressly  chosen  with  the  view  of  making 
what  might  be  considered  a  decisive  comparative  experi- 
1  In  all  cases  nautical  miles  are  meant. 


294:  SOUND. 

ment  between  horns  and  guns  as  instruments  for  fog- 
signaling.  The  distinct  report  of  the  12  o'clock  gun 
fired  at  Dover  on  the  19th  suggested  this  comparison,  and 
through  the  prompt  courtesy  of  General  Sir  A.  Horsford 
we  were  enabled  to  carry  it  out.  At  12.30  precisely  the 
puff  of  an  18-pounder,  with  5  3-lb.  charge,  was  seen  at 
Dover  Castle,  which  was  about  a  mile  farther  off  than  the 
South  Foreland.  Thirty-six  seconds  afterward  the  loud 
report  of  the  gun  was  heard,  its  complete  superiority  over 
the  trumpets  being  thus,  to  all  appearance,  demonstrated. 

We  clinched  this  observation  by  steaming  out  to  a 
distance  of  8^  miles,  where  the  report  of  a  second  gun 
was  well  heard  by  all  of  us.  At  a  distance  of  10  miles  the 
report  of  a  third  gun  was  heard  by  some,  and  at  9.7  miles 
the  report  of  a  fourth  gun  was  heard  by  all. 

The  result  seemed  perfectly  decisive.  Applying  the 
law  of  inverse  squares,  the  sound  of  the  gun  at  a  distance 
of  6  miles  from  the  Foreland  must  have  had  more  than 
two  and  a  half  times  the  intensity  of  the  sound  of  the 
trumpets.  It  would  not  have  been  rash  under  the  circum- 
stances to  have  reported  without  qualification  the  su- 
periority of  the  gun  as  a  fog-signal.  Xo  single  experi- 
ment is,  to  my  knowledge,  on  record  to  prove  that  a  sound 
once  predominant  would  not  be  always  predominant,  or 
that  the  atmosphere  on  different  days  would  show  pref- 
erences to  different  sounds.  On  many  subsequent  occa- 
sions, however,  the  sound  of  the  horns  proved  distinctly 
superior  to  that  of  the  gun.  This  selective  power  of  the 
atmosphere  revealed  itself  more  strikingly  in  our  autumn 
experiments  than  in  our  summer  ones;  and  it  was  some- 
times illustrated  within  a  few  hours  of  the  same  day:  of 
two  sounds,  for  example,  one  might  have  the  greatest 
range  at  10  A.M.,  and  the  other  the  greatest  range  at  2  P.M. 

In  the  experiments  on  May  19th  and  20th  the  superior- 
ity of  the  trumpets  over  the  whistles  was  decided ;  and  in- 


RANGE  OF  GUNS,   TRUMPETS,   AND  WHISTLES.     295 

deed,  with  few  exceptions,  this  superiority  was  maintained 
throughout  the  inquiry.  But  there  were  exceptions.  On 
June  2d,  for  example,  the  whistles  rose  in  several  instances 
to  full  equality  with,  and  on  rare  occasions  subsequently 
even  surpassed  the  horns.  The  sounds  were  varied  from 
day  to  day,  and  various  shiftings  of  the  horns  and  reeds 
were  resorted  to,  with  a  view  of  bringing  out  their  maxi- 
mum power.  On  the  date  last  mentioned  a  single  horn 
was  sounded,  two  were  sounded,  and  three  were  sounded 
together;  but  the  utmost  range  of  the  loudest  sound,  even 
with  the  paddles  stopped,  did  not  exceed  6  miles.  With 
the  view  of  concentrating  their  power,  the  axes  of  the 
horns  had  been  pointed  in  the  same  direction,  and,  unless 
stated  to  the  contrary,  this  in  all  subsequent  experiments 
was  the  case. 

On  June  3d  the  three  guns  already  referred  to  were 
permanently  mounted  at  the  South  Foreland.  They  were 
ably  served  by  gunners  from  Dover  Castle. 

On  the  same  day  dense  clouds  quite  covered  the  firma- 
ment, some  of  them  particularly  black  and  threatening,  but 
a  marked  advance  was  observed  in  the  transmissive  power 
of  the  air.  At  a  distance  of  6  miles  the  horn-sounds  were 
not  quite  quenched  by  the  paddle-noises;  at  8  miles  the 
whistles  were  heard,  and  the  horns  better  heard;  while  at 
9  miles,  with  the  paddles  stopped,  the  horn-sounds  alone 
were  fairly  audible.  During  the  day's  observations  a 
remarkable  and  instructive  phenomenon  was  observed. 
Over  us  rapidly  passed  a  torrential  shower  of  rain,  which, 
according  to  Derham,  is  a  potent  damper  of  sound.  We 
could,  however,  notice  no  subsidence  of  intensity  as  the 
shower  passed.  It  is  even  probable  that,  had  our  minds 
been  free  from  bias,  we  should  have  noticed  an  augmenta- 
tion of  the  sound,  such  as  occurred  with  the  greatest  dis- 
tinctness on  various  subsequent  occasions  during  violent 
rain. 


'296  SOUND. 

The  influence  of  "  beats  "  was  tried  on  June  3d,  by 
throwing  the  horns  slightly  out  of  unison;  but  though  the 
beats  rendered  the  sound  characteristic,  they  did  not  seem 
to  augment  the  range.  At  a  distance  from  the  station 
curious  fluctuations  of  intensity  were  noticed.  Kot  only 
did  the  different  blasts  vary  in  strength,  but  sudden  swell- 
ings and  fallings  off,  even  of  the  same  blast,  were  observed. 
This  was  not  due  to  any  variation  on  the  part  of  the  in- 
struments, but  purely  to  the  changes  of  the  medium  trav- 
ersed by  the  sound.  What  these  changes  were  shall  be 
indicated  subsequently. 

The  range  of  our  best  horns  on  June  10th  was  8f  miles. 
The  guns  at  this  distance  were  very  feeble.  That  the 
loudness  of  the  sound  depends  on  the  shape  of  the  gun 
was  proved  by  the  fact  that  thus  far  the  howitzer,  with  a 
3-lb.  charge,  proved  more  effective  than  the  other  guns. 

On  June  25th  a  gradual  improvement  in  the  transmis- 
sive  power  of  the  air  was  observed  from  morning  to  even- 
ing; but  at  the  last  the  maximum  range  was  only  moder- 
ate. The  fluctuations  in  the  strength  of  the  sound  were 
remarkable,  sometimes  sinking  to  inaudibility  and  then  ris- 
ing to  loudness.  A  similar  effect,  due  to  a  similar  cause,  is 
often  noticed  with  church-bells.  The  acoustic  transpar- 
ency of  the  air  was  still  further  augmented  on  the  26th: 
at  a  distance  of  9^  miles  from  the  station  the  whistles  and 
horns  were  plainly  heard  against  a  wind  with  a  force  of  4 ; 
while  on  the  25th,  with  a  favoring  wind,  the  maximum 
range  was  only  6£  miles.  Plainly,  therefore,  something 
else  than  the  wind  must  be  influential  in  determining  the 
range  of  the  sound. 

On  Tuesday,  July  1st,  observations  were  made  on  the 
decay  of  the  sound  at  various  angular  distances  from  the 
axis  of  the  horn.  As  might  be  expected  the  sound  in  the 
axis  was  loudest,  the  decay  being  gradual  on  both  sides. 


VARIATIONS  OF  RANGE.  297 

In  the  case  of  the  gun,  however,  the  direction  of  pointing 
has  very  little  influence. 

The  day  was  acoustically  clear;  at  a  distance  of  10 
miles  the  horn  yielded  a  plain  sound,  while  the  American 
whistle  seemed  to  surpass  the  horn.  Dense  haze  at  this 
time  quite  hid  the  Foreland.  At  10£  miles  occasional 
blasts  of  the  horn  came  to  us,  but  after  a  time  all  sound 
ceased  to  be  audible;  it  seemed  as  if  the  air,  after  having 
been  exceedingly  transparent,  had  become  gradually  more 
opaque  to  the  sound. 

At  4.45  P.  M.  we  took  the  master  of  the  Varne  light- 
ship on  board  the  Irene.  He  and  his  company  had  heard 
the  sound  at  intervals  during  the  day,  although  he  was 
dead  to  windward  and  distant  12f  miles  from  the  source  of 
sound. 

Here  a  word  of  reflection  on  our  observations  may  be 
fitly  introduced.  It  is,  as  already  shown,  an  opinion  en- 
tertained in  high  quarters  that  the  waves  of  sound  are  re- 
flected at  the  limiting  surfaces  of  the  minute  particles 
which  constitute  haze  and  fog,  the  alleged  waste  of  sound 
in  fog  being  thus  explained.  If,  however,  this  be  an  effi- 
cient practical  cause  of  the  stoppage  of  sound,  and  if  clear 
calm  air  be,  as  alleged,  the  best  vehicle,  it  would  be  impos- 
sible to  understand  how  to-day,  in  a  thick  haze,  the  sound 
reached  a  distance  of  12f  miles,  while  on  May  20th,  in  a 
calm  and  hazeless  atmosphere,  the  maximum  range  was 
only  fom  5  to  6  miles.  Such  facts  foreshadow  a  revolu- 
tion in  our  notions  regarding  the  action  of  haze  and  fogs 
upon  sound. 

An  interval  of  12  hours  sufficed  to  change  in  a  surpris- 
ing degree  the  acoustic  transparency  of  the  air.  On  the 
1st  of  July  the  sound  had  a  range  of  nearly  13  miles;  on 
the  2d  the  range  did  not  exceed  4  miles. 


298  SOUND. 

§  3.  Contradictory  Results. 

Thus  far  the  investigation  proceeded  with  hardly  a 
gleam  of  a  principle  to  connect  the  inconstant  results. 
The  distance  reached  by  the  sound  on  the  19th  of  May 
was  3^  miles;  on  the  20th  it  was  5^  miles;  on  the  2d  of 
June  6  miles;  on  the  3d  more  than  9  miles;  on  the  10th 
it  was  also  9  miles;  on  the  25th  it  fell  to  6^  miles;  on  the 
26th  it  rose  again  to  more  than  9^  miles;  on  the  1st  of 
July,  as  we  have  just  seen,  it  reached  12f ,  whereas  on  the 
2d  the  range  shrunk  to  4  miles.  None  of  the  meteoro- 
logical agents  observed  could  be  singled  out  as  the  cause 
of  these  fluctuations.  The  wind  exerts  an  acknowledged 
power  over  sound,  but  it  could  not  account  for  these  phe- 
nomena. On  the  25th  of  June,  for  example,  when  the 
range  was  only  6^  miles,  the  wind  was  favorable;  on  the 
26th,  when  the  range  exceeded  9^  miles,  it  was  opposed 
to  the  sound.  Nor  could  the  varying  optical  clearness  of 
the  atmosphere  be  invoked  as  an  explanation;  for  on  July 
1st,  when  the  range  was  12f  miles,  a  thick  haze  hid  the 
white  cliffs  of  the  Foreland,  while  on  many  other  days, 
when  the  acoustic  range  was  not  half  so  great,  the  atmos- 
phere was  optically  clear.  Up  to  July  3d  all  remained 
enigmatical;  but  on  this  date  observations  were  made 
which  seemed  to  me  to  displace  surmise  and  perplexity  by 
the  clearer  light  of  physical  demonstration. 

§  4.  Solution  of  Contradictions. 

On  July  3d  we  first  steamed  to  a  point  2.9  miles  S.  W. 
by  W.  of  the  signal-station.  No  sounds,  not  even  the 
guns,  were  heard  at  this  distance.  At  2  miles  they  were 
equally  inaudible.  But  this  being  a  position  at  which  the 
sounds,  though  strong  in  the  axis  of  the  horn,  invariably 
subsided,  we  steamed  to  the  exact  bearing  from  which  our 
observations  had  been  made  on  July  1st.  At  2.15  P.  M., 


EXTEAORDINARY  CASE  OF  ACOUSTIC  OPACITY.    299 

and  at  a  distance  of  3|  miles  from  the  station,  with  calm, 
clear  air  and  a  smooth  sea,  the  horns  and  whistle  (Ameri- 
can) were  sounded,  but  they  were  inaudible.  Surprised  at 
this  result,  I  signaled  for  the  guns.  They  were  all  fired, 
but,  though  the  smoke  seemed  at  hand,  no  sound  whatever 
reached  us.  On  July  1st,  in  this  bearing,  the  observed 
range  of  both  horns  and  guns  was  10£  miles,  while  on  the 
bearing  of  the  Yarne  light-vessel  it  was  nearly  13  miles. 
We  steamed  in  to  3  miles,  paused,  and  listened  with  all 
attention;  but  neither  horn  nor  whistle  was  heard.  The 
guns  were  again  signaled  for;  five  of  them  were  fired  in 
succession,  but  not  one  of  them  was  heard.  We  steamed 
on  in  the  same  bearing  to  2  miles,  and  had  the  guns  fired 
point-blank  at  us.  The  howitzer  and  the  mortar,  with 
3-lb.  charges,  yielded  a  feeble  thud,  while  the  18-pounder 
was  wholly  unheard.  Applying  the  law  of  inverse  squares, 
it  follows  that,  with  the  air  and  sea,  according  to  accepted 
notions,  in  a  far  worse  condition,  the  sound  at  2  miles'  dis- 
tance on  July  1st  must  have  had  more  than  forty  times  the 
intensity  which  it  possessed  at  the  same  distance  at  3  p.  M. 
on  the  3d. 

"  On  smooth  water,"  says  Sir  John  Herschel,  "  sound 
is  propagated  with  remarkable  clearness  and  strength." 
Here  was  the  condition;  still,  with  the  Foreland  so  close  to 
us,  the  sea  so  smooth,  and  the  air  so  transparent,  it  was 
difficult  to  realize  that  the  guns  had  been  fired  or  the 
trumpets  blown  at  all.  What  could  be  the  reason?  Had 
the  sound  been  converted  by  internal  friction  into  heat? 
or  had  it  been  wasted  in  partial  reflections  at  the  limiting 
surfaces  of  non-homogeneous  masses  of  air?  I  ventured, 
two  or  three  years  ago,  to  say  something  regarding  the 
function  of  the  Imagination  in  Science,  and,  notwithstand- 
ing the  care  then  taken,  to  define  and  illustrate  its  real 
province,  some  persons,  among  whom  were  one  or  two 
able  men,  deemed  me  loose  and  illogical.  They  mis- 


300  SOUND. 

understood  me.  The  faculty  to  which  I  referred  was 
that  power  of  visualizing  processes  in  space,  and  the  rela- 
tions of  space  itself,  which  must  be  possessed  by  all  great 
physicists  and  geometers.  Looking,  for  example,  at  two 
pieces  of  polished  steel,  we  have  not  a  sense,  or  the  rudi- 
ment of  a  sense,  to  distinguish  the  inner  condition  of  the 
one  from  that  of  the  other.  And  yet  they  may  differ 
materially,  for  one  may  be  a  magnet,  the  other  not.  What 
enabled  Ampere  to  surround  the  atoms  of  such  a  magnet 
with  channels  in  which  electric  currents  ceaselessly  run, 
and  to  deduce  from  these  pictured  currents  all  the  phe- 
nomena of  ordinary  magnetism?  "What  enabled  Faraday 
to  visualize  his  lines  of  force,  and  make  his  mental  pic- 
ture a  guide  to  discoveries  which  have  rendered  his  name 
immortal?  Assuredly  it  was  the  disciplined  imagination. 
Figure  the  observers  on  the  deck  of  the  Irene,  with 
the  invisible  air  stretching  between  them  and  the  South 
Foreland,  knowing  that  it  contained  something  which 
stifled  the  sound,  but  not  knowing  what  that  something 
is.  Their  senses  are  not  of  the  least  use  to  them;  nor 
could  all  the  philosophical  instruments  in  the  world  ren- 
der them  any  assistance.  They  could  not,  in  fact,  take  a 
single  step  toward  the  solution  without  the  formation  of  a 
mental  image — in  other  words,  without  the  exercise  of  the 
imagination. 

Sulphur,  in  homogeneous  crystals,  is  exceedingly  trans- 
parent to  radiant  heat,  whereas  the  ordinary  brimstone  of 
commerce  is  highly  impervious  to  it — the  reason  being 
that  the  brimstone  does  not  possess  the  molecular  con- 
tinuity of  the  crystal,  but  is  a  mere  aggregate  of  minute 
grains  not  in  perfect  optical  contact  with  each  other. 
Where  this  is  the  case,  a  portion  of  the  heat  is  always 
reflected  on  entering  and  on  quitting  a  grain ;  hence,  when 
the  grains  are  minute  and  numerous,  this  reflection  is  so 
often  repeated  that  the  heat  is  entirely  wasted  before  it 


ANALOGIES  OF  SOUND,   LIGHT,   AND  HEAT.       301 

can  plunge  to  any  depth  into  the  substance.  The  same 
remark  applies  to  snow,  foam,  clouds,  and  common  salt, 
indeed,  to  all  transparent  substances  in  powder;  they  are 
all  impervious  to  light,  not  through  the  immediate  absorp- 
tion or  extinction  of  light,  but  through  repeated  inter- 
nal reflection. 

Humboldt,  in  his  observations  at  the  Falls  of  the 
Orinoco,  is  known  to  have  applied  these  principles  to 
sound.  He  found  the  noise  of  the  falls  far  louder  by 
night  than  by  day,  though  in  that  region  the  night  is  far 
noisier  than  the  day.  The  plain  between  him  and  the 
falls  consisted  of  spaces  of  grass  and  rock  intermingled. 
In  the  heat  of  the  day  he  found  the  temperature  of  the 
rock  to  be  considerably  higher  than  that  of  the  grass. 
Over  every  heated  rock,  he  concluded,  rose  a  column  of 
air  rarefied  by  the  heat;  its  place  being  supplied  by  the 
descent  of  heavier  air.  He  ascribed  the  deadening  of 
the  sound  to  the  reflections  which  it  endured  at  the  limit- 
ing surfaces  of  the  rarer  and  denser  air.  This  philo- 
sophical explanation  made  it  generally  known  that  a  non- 
homogeneous  atmosphere  is  unfavorable  to  the  transmis- 
sion of  sound. 

But  what  on  July  3d,  not  with  the  variously-heated 
plain  of  Antures,  but  with  a  calm  sea  as  a  basis  for  the 
atmosphere,  could  so  destroy  its  homogeneity  as  to  enable 
it  to  quench  in  so  short  a  distance  so  vast  a  body  of  sound? 
My  course  of  thought  at  the  time  was  thus  determined: 
As  I  stood  upon  the  deck  of  the  Irene  pondering  the 
question,  I  became  conscious  of  the  exceeding  power  of 
the  sun  beating  against  my  back  and  heating  the  objects 
near  me.  Beams  of  equal  power  were  falling  on  the  sea, 
and  must  have  produced  copious  evaporation.  That  the 
vapor  generated  should  so  rise  and  mingle  with  the  air 
as  to  form  an  absolutely  homogeneous  medium,  was  in  the 
highest  degree  improbable.  It  would  be  sure,  I  thought, 


302  SOUND. 

to  rise  in  invisible  streams,  breaking  through  the  super- 
incumbent air  now  at  one  point,  now  at  another,  thus  ren- 
dering the  air  flocculent  with  wreaths  and  striae,  charged 
in  different  degrees  with  the  buoyant  vapor.  At  the 
limiting  surfaces  of  these  spaces,  though  invisible,  we 
should  have  the  conditions  necessary  to  the  production  of 
partial  echoes  and  the  consequent  waste  of  sound.  As- 
cending and  descending  air-currents,  of  different  tempera- 
tures, as  far  as  they  existed,  would  also  contribute  to  the 
effect. 

Curiously  enough,  the  conditions  necessary  for  the  test- 
ing of  this  explanation  immediately  set  in.  At  3.15  p.  M. 
a  solitary  cloud  threw  itself  athwart  the  sun,  and  shaded 
the  entire  space  between  us  and  the  South  Foreland. 
The  heating  of  the  water  and  the  production  of  vapor- 
and  air-currents  were  checked  by  the  interposition  of  this 
screen;  hence  the  probability  of  suddenly-improved  trans- 
mission. To  test  this  inference,  the  steamer  was  imme- 
diately turned  and  urged  back  to  our  last  position  of  in- 
audibility. The  sounds,  as  I  expected,  were  distinctly 
though  faintly  heard.  This  was  at  3  miles'  distance.  At 
3f  miles,  the  guns  were  fired,  both  point-blank  and  ele- 
vated. The  faintest  pop  was  all  that  we  heard;  but  we 
did  hear  a  pop,  whereas  we  had  previously  heard  nothing, 
either  here  or  three-quarters  of  a  mile  nearer.  We  steamed 
out  to  4|  miles,  where  the  sounds  were  for  a  moment  faint- 
ly heard;  but  they  fell  away  as  we  waited;  and  though 
the  greatest  quietness  reigned  on  board,  and  though  the 
sea  was  without  a  ripple,  we  could  hear  nothing.  We 
could  plainly  see  the  steam-puffs  which  announced  the  be- 
ginning and  the  end  of  a  series  of  trumpet-blasts,  but  the 
blasts  themselves  were  quite  inaudible. 

It  was  now  4  p.  M.,  and  my  intention  at  first  was  to 
halt  at  this  distance,  which  was  beyond  the  sound-range, 
but  not  far  beyond  it,  and  see  whether  the  lowering  of  the 


GREAT  CHANGE  OF  ACOUSTIC  TRANSPARENCY.    303 

sun  would  not  restore  the  power  of  the  atmosphere  to 
transmit  the  sound.  But  after  waiting  a  little  the  anchor- 
ing of  a  boat  was  suggested,  so  as  to  liberate  the  steamer 
for  other  work;  and  though  loath  to  lose  the  anticipated 
revival  of  the  sounds  myself,  I  agreed  to  this  arrangement. 
Two  men  were  placed  in  the  boat  and  requested  to  give  all 
attention,  so  as  to  hear  the  sound  if  possible.  With  per- 
fect stillness  around  them  they  heard  nothing.  They 
were  then  instructed  to  hoist  a  signal  if  they  should  hear 
the  sounds,  and  to  keep  it  hoisted  as  long  as  the  sounds 
continued. 

At  4.45  we  quitted  them  and  steamed  toward  the 
South  Sand  Head  light-ship.  Precisely  15  minutes  after 
we  had  separated  from  them  the  flag  was  hoisted;  the 
sound  had  at  length  succeeded  in  piercing  the  body  of  air 
between  the  boat  and  the  shore. 

We  continued  our  journey  to  the  light-ship,  went  on 
board,  heard  the  report  of  the  lightsmen,  and  returned  to 
our  anchored  boat.  We  then  learned  that  when  the  flag 
was  hoisted  the  horn-sounds  were  heard,  that  they  were 
succeeded  after  a  little  time  by  the  whistle-sounds,  and  that 
both  increased  in  intensity  as  the  evening  advanced.  On 
our  arrival,  of  course  we  heard  the  sounds  ourselves. 

We  pushed  the  test  further  by  steaming  farther  out. 
At  5f  miles  we  halted  and  heard  the  sounds:  at  6  miles 
we  heard  them  distinctly,  but  so  feebly  that  we  thought  we 
had  reached  the  limit  of  the  sound-range;  but  while  we 
waited  the  sounds  rose  in  power.  We  steamed  to  the 
Varne  buoy,  which  is  7f  miles  from  the  signal-station,  and 
heard  the  sounds  there  better  than  at  6  miles'  distance. 
We  continued  our  course  outward  to  10  miles,  halted 
there  for  a  brief  interval,  but  heard  nothing. 

Steaming,  however,  on  to  the  Varne  light-ship,  which 
is  situated  at  the  other  end  of  the  Yarne  shoal,  we  hailed 
the  master,  and  were  informed  by  him  that  up  to  5  P.  H. 


304:  SOUND. 

nothing  had  been  heard,  but  that  at  that  hour  the  sounds 
began  to  be  audible.  He  described  one  of  them  as  "  very 
gross,  resembling  the  bellowing  of  a  bull,"  which  very  ac- 
curately characterizes  the  sound  of  the  large  American 
steam-whistle.  At  the  Varne  light-ship,  therefore,  the 
sounds  had  been  heard  toward  the  close  of  the  day,  though 
it  is  12f  miles  from  the  signal-station.  I  think  it  prob- 
able that,  at  a  point  2  miles  from  the  Foreland,  the  sound 
at  5  P.  M.  possessed  fifty  times  the  intensity  which  it  pos- 
sessed at  2  p.  M.  To  such  undreamed-of  fluctuations  is 
the  atmosphere  liable.  On  our  return  to  Dover  Bay,  at 
10  P.  M.,  we  heard  the  sounds,  not  only  distinct  but  loud, 
where  nothing  could  be  heard  in  the  morning. 

§  5.  Other  Remarkable  Instances  of  Acoustic  Opacity. 

In  his  excellent  lecture  entitled  "  Wirkungen  aus  der 
Feme,"  Dove  has  collected  some  striking  cases  of  the  in- 
terception of  sound.  The  Duke  of  Argyll  has  also  favored 
me  with  some  highly-interesting  illustrations.  But  noth- 
ing of  this  description  that  I  have  read  equals  in  point  of 
interest  the  following  account  of  the  battle  of  Gaines's 
Farm,  for  which  I  am  indebted  to  the  Eector  of  the  Uni- 
versity of  Virginia: 

"  LYNCHBURG,  VIRGINIA,  March  19, 1874. 

"  SIR:  I  have  just  read  with  great  interest  your  lec- 
ture of  January  16th,  on  the  acoustic  transparency  and 
opacity  of  the  atmosphere.  The  remarkable  observations 
you  mention  induce  me  to  state  to  you  a  fact  which  I 
have  occasionally  mentioned,  but  always,  where  I  am  not 
well  known,  with  the  apprehension  that  my  veracity  would 
be  questioned.  It  made  a  strong  impression  on  me  at  the 
time,  but  was  an  insoluble  mystery  until  your  discourse 
gave  me  a  possible  solution. 

"  On  the  afternoon  of  June  28,  1862,  I  rode,  in  com- 


NOISE  OF  BATTLE  UNHEARD.  305 

pany  with  General  G.  "W.  Randolph,  then  Secretary  of 
AVar  of  the  Confederate  States,  to  Price's  house,  about 
nine  miles  from  Richmond;  the  evening  before  General 
Lee  had  begun  his  attack  on  McClellan's  army,  by  cross- 
ing the  Chickahominy  about  four  miles  above  Price's,  and 
driving  in  McClellan's  right  wing.  The  battle  of  Gaines's 
Farm  was  fought  the  afternoon  to  which  I  refer.  The 
valley  of  the  Chickahominy  is  about  one  and  a  half  miles 
wide  from  hill-top  to  hill-top.  Price's  is  on  one  hill-top, 
that  nearest  to  Richmond;  Gaines's  Farm,  just  opposite,  is 
on  the  other,  reaching  back  in  a  plateau  to  Cold  Harbor. 

"  Looking  across  the  valley  I  saw  a  good  deal  of  the 
battle,  Lee's  right  resting  in  the  valley,  the  Federal  left 
wing  the  same.  My  line  of  vision  was  nearly  in  the  line 
of  the  lines  of  battle.  I  saw  the  advance  of  the  Confeder- 
ates, their  repulse  two  or  three  times,  and  in  the  gray  of 
the  evening  the  final  retreat  of  the  Federal  forces. 

"  I  distinctly  saw  the  musket-fire  of  both  lines,  the 
smoke,  individual  discharges,  the  flash  of  the  guns.  I  saw 
batteries  of  artillery  on  both  sides  come  into  action  and 
fire  rapidly.  Several  field-batteries  on  each  side  were 
plainly  in  sight.  Many  more  were  hid  by  the  timber 
which  bounded  the  range  of  vision. 

"  Yet  looking  for  nearly  two  hours,  from  about  5  to  7 
p.  M.  on  a  midsummer  afternoon,  at  a  battle  in  which  at 
least  50,000  men  were  actually  engaged,  and  doubtless  at 
least  100  pieces  of  field-artillery,  through  an  atmosphere 
optically  as  limpid  as  possible,  not  a  single  sound  of  the 
battle  was  audible  to  General  Randolph  and  myself.  I 
remarked  it  to  him  at  the  time  as  astonishing. 

"  Between  me  and  the  battle  was  the  deep  broad  val- 
ley of  the  Chickahominy,  partly  a  swamp  shaded  from  the 
declining  sun  by  the  hills  and  forest  in  the  west  (my  side). 
Part  of  the  valley  on  each  side  of  the  swamp  was  cleared; 
some  in  cultivation,  some  not.  Here  were  conditions  capa- 


306  SOUND. 

ble  of  providing  several  belts  of  air,  varying  in  the  amount 
of  watery  vapor  (and  probably  in  temperature),  arranged 
like  laminae  at  right  angles  to  the  acoustic  waves  as  they 
came  from  the  battle-field  to  me. 

"  Kespectfully, 

"  Your  obedient  servant, 

"  K.  G.  H.  KEAN. 
"PROF.  JOHN  TYNDALL." 

I  learn  from  a  subsequent  letter  that  during  the  battle 
the  air  was  still. — J.  T. 

§  6.  Echoes  from  Invisible  Acoustic  Clouds. 

But  both  the  argument  and  the  phenomena  have  a 
complementary  side,  which  we  have  now  to  consider.  A 
stratum  of  air  less  than  3  miles  thick  on  a  calm  day  has 
been  proved  competent  to  stifle  both  the  cannonade  and 
the  horn-sounds  employed  at  the  South  Foreland;  while, 
according  to  the  foregoing  explanation,  this  result  was  due 
to  the  reflection  of  the  sound  from  invisible  acoustic  clouds 
which  filled  the  atmosphere  on  a  day  of  perfect  optical 
transparency.  But,  granting  this,  it  is  incredible  that  so 
great  a  body  of  sound  could  utterly  disappear  in  so  short 
a  distance  without  rendering  some  account  of  itself.  Sup- 
posing, then,  instead  of  placing  ourselves  behind  the  acous- 
tic cloud,  we  were  to  place  ourselves  in  front  of  it,  might 
we  not,  in  accordance  with  the  law  of  conservation,  expect 
to  receive  by  reflection  the  sound  which  had  failed  to 
reach  us  by  transmission?  The  case  would  then  be  strict- 
ly analogous  to  the  reflection  of  light  from  an  ordinary 
cloud  to  an  observer  between  it  and  the  sun. 

My  first  care  in  the  early  part  of  the  day  in  question 
was  to  assure  myself  that  our  inability  to  hear  the  sound 
did  not  arise  from  any  derangement  of  the  instruments  on 
shore.  'Accompanied  by  the  private  secretary  of  the 


ACOUSTIC  CLOUDS.  307 

Deputy  Master  of  the  Trinity  House,  at  1  p.  M.  I  was 
rowed  to  the  shore,  and  landed  at  the  base  of  the  South 
Foreland  Cliff.  The  body  of  air  which  had  already  shown 
such  extraordinary  power  to  intercept  the  sound,  and 
which  manifested  this  power  still  more  impressively  later 
in  the  day,  was  now  in  front  of  us.  On  it  the  sonorous 
waves  impinged,  and  from  it  they  were  sent  back  with 
astonishing  intensity.  The  instruments,  hidden  from  view, 
were  on  the  summit  of  a  cliff  235  feet  above  us,  the  sea 
was  smooth  and  clear  of  ships,  the  atmosphere  was  with- 
out a  cloud,  and  there  was  no  object  in  sight  which  could 
possibly  produce  the  observed  effect.  From  the  perfectly 
transparent  air  the  echoes  came,  at  first  with  a  strength 
apparently  little  less  than  that  of  the  direct  sound,  and 
then  dying  away.  A  remark  made  by  my  talented  com- 
panion in  his  note-book  at  the  time  shows  how  the  phe- 
nomenon affected  him:  "  Beyond  saying  that  the  echoes 
seemed  to  come  from  the  expanse  of  ocean,  it  did  not 
appear  possible  to  indicate  any  more  definite  point  of 
reflection."  Indeed  no  such  point  was  to  be  seen;  the 
echoes  reached  us,  as  if  by  magic,  from  the  invisible 
acoustic  clouds  with  which  the  optically  transparent  at- 
mosphere was  filled.  The  existence  of  such  clouds  in  all 
weathers,  whether  optically  cloudy  or  serene,  is  one  of  the 
most  important  points  established  by  this  inquiry. 

Here,  in  my  opinion,  we  have  the  key  to  many  of  the 
mysteries  and  discrepancies  of  evidence  which  beset  this 
question.  The  foregoing  observations  show  that  there  is 
no  need  to  doubt  either  the  veracity  or  the  ability  of  the 
conflicting  witnesses,  for  the  variations  of  the  atmosphere 
are  more  than  sufficient  to  account  for  theirs.  The  mis- 
take, indeed,  hitherto  has  been,  not  in  reporting  incorrect- 
ly, but  in  neglecting  the  monotonous  operation  of  repeat- 
ing the  observations  during  a  sufficient  time.  I  shall  have 
occasion  to  remark  subsequently  on  the  mischief  likely  to 


308  SOUND. 

arise  from  giving  instructions  to  mariners  founded  on 
observations  of  this  incomplete  character,. 

It  required,  however,  long  pondering  and  repeated 
observation  before  this  conclusion  took  firm  root  in  my 
mind;  for  it  was  opposed  to  the  results  of  great  observers, 
and  to  the  statements  of  celebrated  writers.  In  science 
as  elsewhere,  a  mind  of  any  depth  which  accepts  a  doc- 
trine undoubtedly,  discards  it  unwillingly.  The  question 
of  aerial  echoes  has  an  historic  interest.  While  cloud- 
echoes  have  been  accepted  as  demonstrated  by  observa- 
tion, it  has  been  hitherto  held  as  established  that  audible 
echoes  have  been  accepted  as  demonstrated  by  observa- 
opinion  to  the  admirable  report  of  Arago  on  the  experi- 
ments made  to  determine  the  velocity  of  sound  at  Mont- 
lhery and  Villejuif  in  1822. 1  Arago's  account  of  the 
phenomenon  observed  by  him  and  his  colleagues  is  as  fol- 
lows :  "  Before  ending  this  note  we  will  only  add  that  the 
shots  fired  at  Montlhery  were  accompanied  by  a  rumbling 
like  that  of  thunder,  which  lasted  from  20  to  25  sec- 
onds. Nothing  of  this  kind  occurred  at  Villejuif.  Once 
we  heard  two  distinct  reports,  a  second  apart,  of  the 
Montlhery  cannon.  In  two  other  cases  the  report  of  the 
same  gun  was  followed  by  a  prolonged  rumbling.  These 

1  Sir  John  Herschel  gives  the  following  account  of  Arago's  observa- 
tion :  "  The  rolling  of  thunder  has  been  attributed  to  echoes  among  the 
clouds ;  and,  if  it  is  considered  that  a  cloud  is  a  collection  of  particles  of 
water,  however  minute,  in  a  liquid  state,  and  therefore  each  individually 
capable  of  reflecting  sound,  there  is  no  reason  why  very  large  sounds 
should  not  be  reverberated  confusedly  (like  bright  lights)  from  a  cloud. 
And  that  such  is  the  case  has  been  ascertained  by  direct  observation  on 
the  sound  of  cannon.  Messrs.  Arago,  Matthieu,  and  Prony,  in  their  ex- 
periments on  the  velocity  of  sound,  observed  that  under  a  perfectly 
clear  sky  the  explosions  of  their  guns  were  always  single  and  sharp ; 
whereas,  when  the  sky  was  overcast,  and  even  when  a  cloud  came  in 
sight  over  any  considerable  part  of  the  horizon,  they  were  frequently 
accompanied  by  a  long-continued  roll  like  thunder." — ("Essay  on 
Sound,"  par.  38.)  The  distant  clouds  would  imply  a  long  interval  be- 
tween sound  and  echo,  but  nothing  of  the  kind  is  reported. 


REPUTED  CLOUD-ECHOES.  309 

phenomena  never  occurred  without  clouds.  Under  a  clear 
sky  the  sounds  were  single  and  instantaneous.  May  we 
not,  therefore,  conclude  that  the  multiple  reports  of  the 
Montlhery  gun  heard  at  Villejuif  were  echoes  from  the 
clouds,  and  may  we  not  accept  this  fact  as  favorable  to 
the  explanation  given  by  certain  physicists  of  the  rolling 
of  thunder? " 

This  explanation  of  the  Montlhery  echoes  is  an  infer- 
ence from  observations  made  at  Villejuif.  The  inference 
requires  qualification.  Some  hundreds  of  cannon-shots 
have  been  fired  at  the  South  Foreland,  many  of  them 
when  the  heavens  were  completely  free  from  clouds,  and 
never  in  a  single  case  has  a  roulement  similar  to  that 
noticed  at  Montlhery  been  absent.  It  follows,  moreover, 
so  hot  upon  the  direct  sound  as  to  present  hardly  a  sensible 
breach  of  continuity  between  the  sound  and  the  echo. 
This  could  not  be  the  case  if  the  clouds  were  its  origin. 
A  reflecting  cloud,  at  the  distance  of  a  mile,  would  leave 
a  silent  interval  of  nearly  ten  seconds  between  sound  and 
echo;  and  had  such  an  interval  been  observed  at  Mont- 
lhery, it  could  hardly  have  escaped  record  by  the  philoso- 
phers stationed  there;  but  they  have  not  recorded  it. 

I  think  both  the  fact  and  the  inference  need  recon- 
sideration. For  our  observations  prove  to  demonstration 
that  air  of  perfect  visual  transparency  is  competent  to 
produce  echoes  of  great  intensity  and  long  duration.  The 
subject  is  worthy  of  additional  illustration.  On  the  8th 
of  October,  as  already  stated,  the  siren  was  established  at 
the  South  Foreland.  I  visited  the  station  on  that  day, 
and  listened  to  its  echoes.  They  were  far  more  power- 
ful than  those  of  the  horn.  Like  the  others  they  were 
perfectly  continuous,  and  faded,  as  if  into  distance,  gradu- 
ally away.  The  direct  sound  seemed  rendered  complex 
and  multitudinous  by  its  echoes,  which  resembled  a  band 
of  trumpeters,  first  responding  close  at  hand,  and  then  re- 


310  SOUND. 

treating  rapidly  toward  the  coast  of  France.  Tke  siren- 
echoes  on  that  day  had  11  seconds',  those  of  the  horn  8 
seconds'  duration. 

In  the  case  of  the  siren,  moreover,  the  reenforcement 
of  the  direct  sound  by  its  echo  was  distinct.  About  a 
second  after  the  commencement  of  the  siren-blast  the  echo 
struck  in  as  a  new  sound.  This  first  echo,  therefore,  must 
have  been  flung  back  by  a  body  of  air  not  more  than  600 
or  700  feet  in  thickness.  The  few  detached  clouds  visible 
at  the  time  were  many  miles  away,  and  could  clearly  have 
had  nothing  to  do  with  the  effect. 

On  the  10th  of  October  I  was  again  at  the  Foreland 
listening  to  the  echoes,  with  results  similar  to  those  just 
described.  On  the  15th  I  had  an  opportunity  of  remark- 
ing something  new  concerning  them  at  Dungeness,  where 
a  horn  similar  to,  but  not  so  powerful  as,  those  at  the 
South  Foreland,  has  been  mounted.  It  rotates  automati- 
cally through  an  arc  of  210°,  halting  at  four  different 
points  on  the  arc  and  emitting  a  blast  of  6  seconds'  dura- 
tion, these  blasts  being  separated  from  each  other  by  inter- 
vals of  silence  of  20  seconds. 

The  new  point  observed  was  this:  as  the  horn  rotated 
the  echoes  were  always  returned  along  the  line  in  which 
the  axis  of  the  horn  pointed.  Standing  either  behind  or 
in  front  of  the  lighthouse  tower,  or  closing  the  eyes  so  as 
to  exclude  all  knowledge  of  the  position  of  the  horn,  the 
direction  of  its  axis  when  sounded  could  always  be  inferred 
from  the  direction  in  which  the. aerial  echoes  reached  the 
shore.  Not  only,  therefore,  is  knowledge  of  direction 
given  by  a  sound,  but  it  may  also  be  given  by  the  aerial 
echoes  of  the  sound. 

On  thelTth  of  October,  at  about  5  p.  M.,  the  air  being 
perfectly  free  from  clouds,  we  rowed  toward  the  Foreland, 
landed,  and  passed  over  the  sea-weed  to  the  base  of  the 
cliff.  As  I  reached  the  base  the  position  of  the  "  Gala- 


AERIAL  ECHOES.  311 

tea  "  was  such  that  an  echo  of  astonishing  intensity  was 
sent  back  from  her  side;  it  came  as  if  from  an  independ- 
ent source  of  sound  established  on  board  the  steamer. 
This  echo  ceased  suddenly,  leaving  the  aerial  echoes  to 
die  gradually  into  silence. 

At  the  base  of  the  cliff  a  series  of  concurrent  observa- 
tions made  the  duration  of  the  aerial  siren-echoes  from  13 
to  14  seconds. 

Lying  on  the  shingle  under  a  projecting  roof  of  chalk, 
the  somewhat  enfeebled  diffracted  sound  reached  me,  and 
I  was  able  to  hear  with  great  distinctness,  about  a  second 
after  the  starting  of  the  siren-blast,  the  echoes  striking  in 
and  reenf  orcing  the  direct  sound.  The  first  rush  of  echoed 
sound  was  very  powerful,  and  it  came,  as  usual,  from  a 
stratum  of  air  600  or  700  feet  in  thickness.  On  again 
testing  the  duration  of  the  echoes,  it  was  found  to  be  from 
14  to  15  seconds.  The  perfect  clearness  of  the  afternoon 
caused  me  to  choose  it  for  the  examination  of  the  echoes. 
It  is  worth  remarking  that  this  was  our  day  of  longest 
echoes,  and  it  was  also  our  day  of  greatest  acoustic  trans- 
parency, this  association  suggesting  that  the  duration  of 
the  echo  is  a  measure  of  the  atmospheric  depths  from 
which  it  comes.  On  no  day,  it  is  to  be  remembered,  was 
the  atmosphere  free  from  invisible  acoustic  clouds;  and 
on  this  day,  and  when  their  presence  did  not  prevent  the 
direct  sound  from  reaching  to  a  distance  of  15  or  16  nau- 
tical miles,  they  were  able  to  send  us  echoes  of  15  seconds' 
duration. 

On  various  occasions,  when  fully  three  miles  from  the 
shore,  the  Foreland  bearing  north,  we  have  had  the  dis- 
tinct echoes  of  the  siren  sent  back  to  us  from  the  cloud- 
less southern  air. 

To  sum  up  this  question  of  aerial  echoes.  The  siren 
sounded  three  blasts  a  minute,  each  of  5  seconds'  duration. 
From  the  number  of  days  and  the  number  of  hours  per 


312  SOUND. 

day  during  which  the  instrument  was  in  action  we  can 
infer  the  number  of  blasts.  They  reached  nearly  twenty 
thousand.  The  blasts  of  the  horns  exceeded  this  number, 
while  hundreds  of  shots  were  fired  from  the  guns.  What- 
ever might  be  the  state  of  the  weather,  cloudy  or  serene, 
stormy  or  calm,  the  aerial  echoes,  though  varying  in 
strength  and  duration  from  day  to  day,  were  never  absent ; 
and  on  many  days,  "  under  a  perfectly  clear  sky,"  they 
reached,  in  the  case  of  the  siren,  an  astonishing  intensity. 
It  is  doubtless  to  these  air-echoes,  and  not  to  cloud-echoes, 
that  the  rolling  of  thunder  is  to  be  ascribed. 

§    7.  Experimental   Demonstration   of  Reflection   from 
Gases. 

Thus  far  we  have  dealt  in  inference  merely,  for  the 
interception  of  sound  through  aerial  reflection  has  never 
been  experimentally  demonstrated ;  and,  indeed,  according 
to  Arago's  observation,  which  has  hitherto  held  undisputed 
possession  of  the  scientific  field,  it  does  not  sensibly  exist. 
But  the  strength  of  science  consists  in  verification,  and  I 
was  anxious  to  submit  the  question  of  aerial  reflection  to 
an  experimental  test.  The  knowledge  gained  in  the  last 
lecture  enables  us  to  apply  such  a  test;  but  as  in  most 
similar  cases,  it  was  not  the  simplest  combinations  that 
were  first  adopted.  Two  gases  of  different  densities  were 
to  be  chosen,  and  I  chose  carbonic  acid  and  coal  gas. 
"With  the  aid  of  my  skillful  assistant,  Mr.  John  Cottrell,  a 
tunnel  was  formed,  across  which  five-and-twenty  layers  of 
carbonic  acid  were  permitted  to  fall,  and  five-and-twenty 
alternate  layers  of  coal-gas  to  rise.  Sound  was  sent 
through  this  tunnel,  making  fifty  passages  from  medium  to 
medium  in  its  course.  These,  I  thought,  would  waste  in 
aerial  echoes  a  sensible  portion  of  sound. 

To  indicate  this  waste  an  objective  test  was  found  in 
one  of  the  sensitive  flames  described  in  the  last  chapter. 


AERIAL  REFLECTION  PROVED  EXPERIMENTALLY.  313 

Acquainted  with  it,  we  are  prepared  to  understand  a 
drawing  and  description  of  the  apparatus  first  employed 
in  the  demonstration  of  aerial  reflection.  The  following 
clear  account  of  the  apparatus  was  given  by  a  writer  in 
Nature,  February  5,  1874: 

"  A  tunnel  1 1'  (Fig.  146),  2  in.  square,  4  ft.  8  in. 
long,  open  at  both  ends,  and  having  a  glass  front,  runs 
through  the  box  abed.  The  spaces  above  and  below  are 
divided  into  cells  opening  into  the  tunnel  by  transverse 
orifices  exactly  corresponding  vertically.  Each  alternate 
cell  of  the  upper  series — the  1st,  3d,  5th,  etc. — communi- 
cates by  a  bent  tube  (e  e  e)  with  a  common  upper  reservoir 
(</),  its  counterpart  cell  in  the  lower  series  having  a  free 
outlet  into  the  air.  In  like  manner  the  2d,  4th,  6th,  etc., 
of  the  lower  series  of  cells  are  connected  by  bent  tubes 
(n  n  n)  with  the  lower  reservoir  (i),  each  having  its  direct 
passage  into  the  air  through  the  cell  immediately  above  it. 
The  gas-distributors  (g  and  i)  are  filled  from  both  ends  at 
the  same  time,  the  upper  with  carbonic-acid  gas,  the  lower 
with  coal-gas,  by  branches  from  their  respective  supply- 
pipes  (/  and  h).  A  well-padded  box  (p)  open  to  the  end 
of  the  tunnel  forms  a  little  cavern,  whence  the  sound- 
waves are  sent  forth  by  an  electric  bell  (dotted  in  the  fig- 
ure). A  few  feet  from  the  other  end  of  the  tunnel,  and 
in  a  direct  line  with  it,  is  a  sensitive  flame  (&),  provided 
with  a  funnel  as  sound-collector,  and  guarded  from  chance 
currents  by  a  shade. 

"  The  bell  was  set  ringing.  The  flame,  with  quick  re- 
sponse to  each  blow  of  the  hammer,  emitted  a  sort  of 
musical  roar,  shortening  and  lengthening  as  the  succes- 
sive sound-pulses  reached  it.  The  gases  were  then  ad- 
mitted. Twenty-five  flat  jets  of  coal-gas  ascended  from 
the  tubes  below,  and  twenty-five  cascades  of  carbonic 
acid  fell  from  the  tubes  above.  That  which  was  an  ho- 
mogeneous medium  had  now  fifty  limiting  surfaces,  from 


314: 


SOUND. 


REFLECTION  FROM  CARBONIC  ACID  AND  COAL  GAS.  315 

each  of  which  a  portion  of  the  sound  was  thrown  back. 
In  a  few  moments  these  successive  reflections  became  so 
effective  that  no  sound  having  sufficient  power  to  affect 
the  flame  could  pierce  the  clear,  optically-transparent, 
but  acoustically-opaque,  atmosphere  in  the  tunnel.  So 
long  as  the  gases  continued  to  flow  the  flame  remained 
perfectly  tranquil.  When  the  supply  was  cut  off,  the 
gases  rapidly  diffused  into  the  air.  The  atmosphere  of 
the  tunnel  became  again  homogeneous,  and  therefore 
acoustically  transparent,  and  the  flame  responded  to  each 
sound-pulse  as  before." 

Not  only  do  gases  of  different  densities  act  thus  upon 
sound,  but  atmospheric  air  in  layers  of  different  tempera- 
tures does  the  same.  Across  a  tunnel  resembling  t  t',  Fig. 
146,  sixty-six  platinum  wires  were  stretched,  all  of  them 
being  in  metallic  connection.  The  bell,  in  its  padded  box, 
was  placed  at  one  end  of  the  tunnel,  and  the  sensitive 
flame  fc,  near  its  flaring  point,  at  the  other.  When  the 
bell  rang  the  flame  flared.  A  current  from  a  strong  vol- 
taic battery  being  sent  through  the  platinum  wires,  they 
became  heated :  layers  of  warm  air  rose  from  them  through 
the  tunnel,  and  immediately  the  agitation  of  the  flame 
was  stilled.  On  stopping  the  current,  the  agitation  recom- 
menced. In  this  experiment  the  platinum  wires  had  not 
reached  a  red  heat.  Employing  half  the  number  and  the 
same  battery,  they  were  raised  to  a  red  heat,  the  action  in 
this  case  upon  the  sound-waves  being  also  energetic.  Em- 
ploying one-third  of  the  number  of  wires,  and  the  same 
strength  of  battery,  the  wires  were  raised  to  a  white  heat. 
Here  also  the  flame  was  immediately  rendered  tranquil  by 
the  stoppage  of  the  sound. 

§  8.  Reflection  from  Vapors. 

But  not  only  do  gases  of  different  densities,  and  air  of 
different  temperatures,  act  thus  upon  sound,  but  air  satu- 


316  SOUND. 

rated  in  different  degrees,  with  the  vapors  of  volatile 
liquids,  can  be  shown  by  experiment  to  produce  the  same 
effect.  Into  the  path  pursued  by  the  carbonic  acid  in  our 
first  experiment  a  flask,  which  I  have  frequently  employed 
to  charge  air  with  vapor,  was  introduced.  Through  a 
volatile  liquid,  partially  filling  the  flask,  air  was  forced  into 
the  tunnel  t  t' ,  which  was  thus  divided  into  spaces  of  air 
saturated  with  the  vapor,  and  other  spaces  in  their  ordi- 
nary condition.  The  action  of  such  a  medium  upon  the 
sound-waves  issuing  from  the  bell  is  very  energetic,  in- 
stantly reducing  the  violently-agitated  flame  to  stillness 
and  steadiness.  The  removal  of  the  heterogeneous  me- 
dium instantly  restores  the  noisy  flaring  of  the  flame. 

A  few  illustrations  of  the  action  of  non-homogeneous 
atmospheres,  produced  by  the  saturation  of  layers  of  air 
with  the  vapors  of  volatile  liquids,  may  follow  here : 

Bisulphide  of  Carbon. — Flame  very  sensitive,  and 
noisily  responsive  to  the  sound.  The  action  of  the  non- 
homogeneous  atmosphere  was  prompt  and  strong,  stilling 
the  agitated  flame. 

Chloroform. — Flame  still  very  sensitive;  action  simi- 
lar to  the  last. 

Iodide  of  Methyl. — Action  prompt  and  energetic. 

Amylene. — Very  fine  action;  a  short  and  violently- 
agitated  flame  was  immediately  rendered  tall  and  quies- 
cent. 

Sulphuric  Ether. — Action  prompt  and  energetic. 

The  vapor  of  water  at  ordinary  temperatures  is  so  small 
in  quantity  and  so  attenuated,  that  it  requires  special 
precaution  to  bring  out  its  action.  But  with  such  pre- 
cautions it  was  found  competent  to  reduce  to  quiescence 
the  sensitive  flame. 

As  the  skill  and  knowledge  of  the  experimenter  aug- 
ment he  is  often  able  to  simplify  his  experimental  combi- 
nations. Thus,  in  the  present  instance,  by  the  suitable 


REFLECTION  FROM  HEATED  AIR  AND  VAPORS.     317 

arrangement  of  the  source  of  sound  and  the  sensitive 
flame,  it  was  found  that  not  only  twenty-five  layers,  but 
three  or  four  layers  of  coal-gas  and  carbonic  acid,  sufficed 
to  still  the  agitated  flame.  Nay,  with  improved  manip- 
ulation, the  action  of  a  single  layer  of  either  gas  was 
rendered  perfectly  sensible.  So  also  as  regards  heated 
layers  of  air,  not  only  were  sixty-six  or  twenty-two 
heated  platinum  wires  found  sufficient,  but  the  heated  air 
from  two  or  three  candle-flames,  or  even  from  a  single 
flame,  or  a  heated  poker,  was  found  perfectly  competent 
to  stop  the  flame's  agitation.  The  same  remark  applies 


FIG.  147. 


to  vapors.  Three  or  four  heated  layers  of  air,  saturated 
with  the  vapor  of  a  volatile  liquid,  stilled  the  flame ;  and, 
by  improved  manipulation,  the  action  of  a  single  saturated 
layer  could  be  rendered  sensible.  In  all  these  cases, 
moreover,  a  small,  high-pitched  reed  might  be  substituted 
for  the  bell. 

My  assistant  has  devised  the  simple  apparatus  sketched 
in  Fig.  147,  for  showing  reflection  by  gases,  vapors,  and 
heated  air.  At  the  end  A  of  the  square  pipe  A  B  is  a  small 


318  SOUND. 

vibrating  reed  of  high  pitch,  the  sound  of  which  violently 
agitates  the  sensitive  flame  /.  To  the  horizontal  tube  g  g' 
are  attached  four  small  burners,  and  above  them  four 
chimneys,  through  which  the  heated  gases  from  the  flames 
can  ascend  into  A  B.  When  the  coverings  of  the  chimneys 
are  removed  and  the  gas  is  ignited,  the  air  within  A  B  is 
rendered  rapidly  non-homogeneous,  and  immediately  stills 
the  agitated  flame. 

The  pipe  A  B  may  be  turned  upside  down,  an  orifice 
seen  between  A  and  B  fitting  up  on  to  the  stand  which  sup- 
ports the  tube.  The  conduit  t  leads  into  a  shallow  rectan- 
gular box,  which  communicates  by  a  series  of  transverse 
apertures  with  A  B.  When  air,  saturated  with  the  vapor 
of  a  volatile  liquid,  is  forced  through  these  apertures,  the 
atmosphere  in  A  B  is  immediately  rendered  heterogeneous, 
the  agitated  flame  being  as  rapidly  stilled. 

In  the  experiments  at  the  South  Foreland,  not  only 
was  it  proved  that  the  acoustic  clouds  stopped  the  sound; 
but,  in  the  proper  position,  the  sounds  which  had  been  re- 
fused transmission  were  received  by  reflection.  I  wished 
very  much  to  render  this  echoed  sound  evident  experi- 
mentally; and  stated  to  my  assistant  that  we  ought  to  be 
able  to  accomplish  this.  Mr.  Cottrell  met  my  desire  by 
the  following  beautiful  experiment,  which  has  been  thus 
described  before  the  Royal  Society: 

"  A  vibrating  reed  B  (Fig.  148)  was  placed  so  as  to 
send  sound-waves  through  a  tin  tube,  38  inches  long,  and 
If  inch  diameter,  in  the  direction  B  A,  the  action  of  the 
sound  being  rendered  manifest  by  its  causing  a  sensitive 
flame  placed  at  F'  to  become  violently  agitated. 

"  The  invisible  heated  layer  immediately  above  the  lu- 
minous portion  of  an  ignited  coal-gas  flame  issuing  from 
an  ordinary  bat's-wing  burner  was  allowed  to  stream  up- 
ward across  the  end  A  of  the  tin  tube.  A  portion  of  the 
sound  issuing  from  the  tube  was  reflected  at  the  limiting 


ECHO  FROM  FLAME. 


319 


surfaces  of  the  heated  layer;  the  part  transmitted  being 
now  only  competent  to  slightly  agitate  the  sensitive  flame 
atr'. 

"  The  heated  layer  was  then  placed  at  such  an  angle 
that  the  reflected  portion  of  the  sound  was  sent  through  a 
second  tin  tube,  A  F  (of  the  same  dimensions  as  B  A). 
Its  action  was  rendered  visible  by  causing  a  second  sensi- 
tive flame  placed  at  the  end  of  the  tube  at  F  to  become  vio- 
lently affected.  This  echo  continued  active  as  long  as  the 
heated  layer  intervened;  but  upon  its  withdrawal  the  sen- 
sitive flame  placed  at  F',  receiving  the  whole  of  the  direct 


pulse,  became  again  violently  agitated,  and  at  the  same 
moment  the  sensitive  flame  at  F,  ceasing  to  be  affected  by 
the  echo,  resumed  its  former  tranquillity. 

"  Exactly  the  same  action  takes  place  when  the  lumi- 
nous portion  of  a  gas-flame  is  made  the  reflecting  layer;  but 
in  the  experiments  above  described  the  invisible  layer 
above  the  flame  only  was  used.  By  proper  adjustment  of 
the  pressure  of  the  gas  the  flame  at  F'  can  be  rendered  so 
moderately  sensitive  to  the  direct  sound-wave  that  the 
portion  transmitted  through  the  reflecting  layer  shall  be 
21 


320  SOUND. 

incompetent  to  affect  the  flame.  Then  by  the  introduction 
and  withdrawal  of  the  bat's-wing  flame  the  two  sensitive 
flames  can  be  rendered  alternately  quiescent  and  strongly 
agitated. 

"  An  illustration  is  here  afforded  of  the  perfect  anal- 
ogy between  light  and  sound;  for  if  a  beam  of  light  be 
projected  from  B  to  F',  and  a  plate  of  glass  be  introduced 
at  A  in  the  exact  position  of  the  reflecting  layer  of  gas, 
the  beam  will  be  divided,  one  portion  being  reflected  in 
the  direction  A  F,  and  the  other  portion  transmitted 
through  the  glass  toward  F',  exactly  as  the  sound-wave  is 
divided  into  a  reflected  and  transmitted  portion  by  the 
layer  of  heated  gas  or  flame." 

Thus  far,  therefore,  we  have  placed  our  subject  in  the 
firm  grasp  of  experiment;  nor  shall  we  find  this  test  fail- 
ing us  further  on. 


PART  II. 

INVESTIGATION  OF  THE  CAUSES  WHICH  HAVE  HITHERTO  BEEN 
SUPPOSED  EFFECTIVE  IN  PREVENTING  THE  TRANSMISSION 
OF  SOUND  THROUGH  THE  ATMOSPHERE. 


Action  of  Hail  and  Rain.— Action  of  Snow. — Action  of  Fog :  Observa- 
tions in  London. — Experiments  on  Artificial  Fogs. — Observations 
on  Fogs  at  the  South  Foreland. — Action  of  Wind. — Atmospheric 
Selection.— Influence  of  Sound-Shadow. 

§  1.  Action  of  Hail  and  Rain. 

In  the  first  part  of  this  chapter  it  was  demonstrated 
that  the  optic  transparency  and  acoustic  transparency  of 
our  atmosphere  were  by  no  means  necessarily  coincident; 
that  on  days  of  marvelous  optical  clearness  the  atmosphere 
may  be  filled  with  impervious  acoustic  clouds,  while  days 


ACTION  OF  HAIL  AND  RAIN.  321 

optically  turbid  may  be  acoustically  clear.  We  have  now 
to  consider,  in  detail,  the  influence  of  various  agents  which 
have  hitherto  been  considered  potent  in  reference  to  the 
transmission  of  sound  through  the  atmosphere. 

Derham,  and  after  him  all  other  writers,  considered 
that  falling  rain  tended  powerfully  to  obstruct  sound.  An 
observation  on  June  3d  has  been  already  referred  to  as 
tending  to  throw  doubt  on  this  conclusion.  Two  other 
crucial  instances  will  suffice  to  show  its  untenability.  On 
the  morning  of  October  8th,  at  7.45  A.  M.,  a  thunderstorm 
accompanied  by  heavy  rain  broke  over  Dover.  But  the 
clouds  subsequently  cleared  away,  and  the  sun  shone 
strongly  on  the  sea.  For  a  time  the  optical  clearness  of 
the  atmosphere  was  extraordinary,  but  it  was  acoustically 
opaque.  At  2.30  p.  M.  a  densely-black  scowl  again  over- 
spread the  heavens  to  the  W.  S.  W.  The  distance  being 
6  miles,  and  all  hushed  on  board,  the  horn  was  heard  very 
feebly,  the  siren  more  distinctly,  while  the  howitzer  was 
better  than  either,  though  not  much  superior  to  the  siren. 

A  squall  approached  us  from  the  west.  In  the  Alps 
or  elsewhere  I  have  rarely  seen  the  heavens  blacker. 
Vast  cumuli  floated  to  the  K.  E.  and  S.  E. ;  vast  streamers 
of  rain  descended  in  the  W.  N.  W. ;  huge  scrolls  of  cloud 
hung  in  the  N. ;  but  spaces  of  blue  were  to  be  seen  to  the 
K  N.  E. 

At  7  miles'  distance  the  siren  and  horn  were  both 
feeble,  while  the  gun  sent  us  a  very  faint  report.  A  dense 
shower  now  enveloped  the  Foreland. 

The  rain  at  length  reached  us,  falling  heavily  all  the 
way  between  us  and  the  Foreland;  but  the  sound,  instead 
of  being  deadened,  rose  perceptibly  in  power.  Hail  was 
now  added  to  the  rain,  and  the  shower  reached  a  tropical 
violence,  the  hailstones  floating  thickly  on  the  flooded 
deck.  In  the  midst  of  this  furious  squall  both  the  horns 
and  the  siren  were  distinctly  heard;  and  as  the  shower 


322  SOUND. 

lightened,  thus  lessening  the  local  pattering,  the  sounds  so 
rose  in  power  that  we  heard  them  at  a  distance  of  7^  miles 
distinctly  louder  than  they  had  been  heard  through  the 
rainless  atmosphere  at  5  miles. 

At  4  P.  M.  the  rain  had  ceased  and  the  sun  shone  clearly 
through  the  calm  air.  At  9  miles'  distance  the  horn  was 
heard  feebly,  the  siren  clearly,  while  the  howitzer  sent  us 
a  loud  report.  All  the  sounds  were  better  heard  at  this 
distance  than  they  had  previously  been  at  5£  miles;  from 
which,  by  the  law  of  inverse  squares,  it  follows  that  the 
intensity  of  the  sound  at  5|  miles'  distance  must  have  been 
augmented  at  least  threefold  by  the  descent  of  the  rain. 

On  the  23d  of  October  our  steamer  had  forsaken  us 
for  shelter,  and  I  sought  to  turn  the  weather  to  account 
by  making  other  observations  on  both  sides  of  the  fog- 
signal  station.  Mr.  Douglass,  the  chief-engineer  of  the 
Trinity  House,  was  good  enough  to  undertake  the  obser- 
vations N.  E.  of  the  Foreland;  while  Mr  Ayers,  the 
assistant  engineer,  walked  in  the  other  direction.  At 
12.50  P.  M.  the  wind  blew  a  gale,  and  broke  into  a  thunder- 
storm with  violent  rain.  Inside  and  outside  the  Cornhill 
Coast-guard  Station,  a  mile  from  the  instruments  in  the 
direction  of  Dover,  Mr.  Ayers  heard  the  sound  of  the 
siren  through  the  storm;  and  after  the  rain  had  ceased, 
all  sounds  were  heard  distinctly  louder  than  before.  Mr. 
Douglass  had  sent  a  fly  before  him  to  Kingsdown,  and  the 
driver  had  been  waiting  for  fifteen  minutes  before  he  ar- 
rived. During  this  time  no  sound  had  been  heard,  though 
40  blasts  had  been  blown  in  the  interval;  nor  had  the 
coast-guard  man  on  duty,  a  practised  observer,  heard  any 
of  them  throughout  the  day.  During  the  thunderstorm, 
and  while  the  rain  was  actually  falling  with  a  violence 
which  Mr.  Douglass  describes  as  perfectly  torrential,  the 
sounds  became  audible  and  were  heard  by  all. 

To  rain,  in  short,  I  have  never  been  able  to  trace  the 


ACTION  OF  SNOW.  323 

slightest  deadening  influence  upon  sound.  The  reputed 
barrier  offered  by  "  thick  weather  "  to  the  passage  of  sound 
was  one  of  the  causes  which  tended  to  produce  hesitation 
in  establishing  sound-signals  on  our  coasts.  It  is  to  be 
hoped  that  the  removal  of  this  error  may  redound  to  the 
advantage  of  coming  generations  of  seafaring  men. 

§  2.  Action  of  Snow. 

Falling  snow,  according  to  Derham,  is  the  most  serious 
obstacle  of  all  to  the  transmission  of  sound.  We  did  not 
extend  our  observations  at  the  South  Foreland  into  snowy 
weather;  but  a  previous  observation  of  my  own  bears  di- 
rectly upon  this  point.  On  Christmas-night,  1859,  I  ar- 
rived at  Chamouni,  through  snow  so  deep  as  to  obliterate 
the  road-fences,  and  to  render  the  labor  of  reaching  the 
village  arduous  in  the  extreme.  On  the  26th  and  27th 
it  fell  heavily.  On  the  27th,  during  a  lull  in  the  storm,  I 
reached  the  Montavert,  sometimes  breast-deep  in  snow. 
On  the  28th,  with  great  difficulty,  two  lines  of  stakes  were 
set  out  across  the  glacier,  with  the  view  of  determining  its 
winter  motion.  On  the  29th  the  entry  in  my  journal, 
written  in  the  morning,  is:  "  Snow,  heavy  snow;  it  must 
have  descended  through  the  entire  night,  the  quantity 
freshly  fallen  is  so  great." 

Under  these  circumstances  I  planted  my  theodolite 
beside  the  Mer  de  Glace,  having  waded  to  my  position 
through  snow,  which,  being  dry,  reached  nearly  to  my 
breast.  Assistants  were  sent  across  the  glacier  with  in- 
structions to  measure  the  displacements  of  a  transverse  line 
of  stakes  planted  previously  in  the  snow.  A  storm  drifted 
up  the  valley,  darkening  the  air  as  it  approached.  It 
reached  us,  the  snow  falling  more  heavily  than  I  had  ever 
seen  it  elsewhere.  It  soon  formed  a  heap  on  the  theodo- 
lite, and  thickly  covered  my  own  clothes.  Here,  then,  was 
a  combination  of  snow  in  the  air,  and  of  soft  fresh  snow 


324  SOUND. 

on  the  ground,  such  as  Derham  could  hardly  have  enjoyed; 
still  through  such  an  atmosphere  I  was  able  to  make  my 
instructions  audible  quite  across  the  glacier,  the  distance 
being  half  a  mile,  while  the  experiment  was  rendered  re- 
ciprocal by  one  of  my  assistants  making  his  voice  audible 
to  me. 

§   3.  Passage  of  Sound  through   Textile  Fabrics,  and 
through  Artificial  Showers. 

The  flakes  here  were  so  thick  that  it  was  only  at  in- 
tervals that  I  was  able  to  pick  up  the  retreating  form's  of 
the  men.  Still  the  air  through  which  the  flakes  fell  was 
continuous.  Did  the  flakes  merely  yield  passively  to  the 
sonorous  waves,  swinging  like  the  particles  of  air  them- 
selves to  and  fro  as  the  sound-waves  passed  them?  Or  did 
the  waves  bend  by  diffraction  round  the  flakes,  and  emerge 
from  them  without  sensible  loss?  Experiment  will  aid  us 
here  by  showing  the  astonishing  facility  with  which  sound 
makes  its  way  among  obstacles,  and  passes  through  tissues, 
so  long  as  the  continuity  of  the  air  in  their  interstices  is 
preserved. 

A  piece  of  millboard  or  of  glass,  a  plank  of  wood,  or  the 
hand,  placed  across  the  open  end  t'  of  the  tunnel  a  b  c  d, 
Fig.  146  (page  314),  intercepts  the  sound  of  the  bell, 
placed  in  the  padded  box  P,  and  stills  the  sensitive 
flame  k. 

An  ordinary  cambric  pocket-handkerchief,  on  the  other 
hand,  placed  across  the  tunnel-end  produced  hardly  an  ap- 
preciable effect  upon  the  sound.  Through  two  layers  of 
the  handkerchief  the  flame  was  strongly  agitated ;  through 
four  layers  it  was  still  agitated;  while  through  six  layers, 
though  nearly  stilled,  it  was  not  entirely  so. 

Dipping  the  same  handkerchief  into  water,  and  stretch- 
ing a  single  wetted  layer  across  the  tunnel-end,  it  stilled 
the  flame  as  effectually  as  the  millboard  or  the  wood. 


PASSAGE  OF  SOUND  THROUGH  TISSUES.         325 

Hence  the  conclusion  that  the  sound-waves  in  the  first  in- 
stance passed  through  the  interstices  of  the  cambric. 

Through  a  single  layer  of  thin  silk  the  sound  passed 
without  sensible  interruption;  through  six  layers  the  flame 
was  strongly  agitated;  while  through  twelve  layers  the 
agitation  was  quite  perceptible. 

A  single  layer  of  this  silk,  when  wetted,  stilled  the 
flame. 

A  layer  of  soft  lint  produced  but  little  effect  upon  the 
sound ;  a  layer  of  thick  flannel  was  almost  equally  ineffect- 
ual. Through  four  layers  of  flannel  the  flame  was  per- 
ceptibly agitated.  Through  a  single  layer  of  green  baize 
the  sound  passed  almost  as  freely  as  through  air;  through 
four  layers  of  the  baize  the  action  was  still  sensible. 
Through  a  layer  of  close  hard  felt,  half  an  inch  thick,  the 
sound-waves  passed  with  sufficient  energy  to  sensibly  agi- 
tate the  flame.  Through  200  layers  of  cotton-net  the 
sound  passed  freely.  I  did  not  witness  these  effects  with- 
out astonishment. 

A  single  layer  of  thin  oiled  silk  stopped  the  sound  and 
stilled  the  flame.  A  leaf  of  common  note-paper,  or  a  five- 
pound  note,  also  stopped  the  sound. 

The  sensitive  flame  is  not  absolutely  necessary  to  these 
experiments.  Let  a  ticking  watch  be  hung  six  inches 
from  the  ear,  a  cambric  handkerchief  dropped  between  it 
and  the  ear  scarcely  sensibly  affects  the  ticking;  a  sheet  of 
oil-skin  or  an  intensely  heated  gas-column  cuts  it  almost 
wholly  off. 

But  though  oiled  silk,  foreign  post,  or  a  bank-note,  can 
stop  the  sound,  a  film  sufficiently  thin  to  yield  freely  to 
the  aerial  pulses  transmits  it.  A  thick  soap-film  produces 
an  obvious  effect  upon  the  sensitive  flame;  a  very  thin  one 
does  not.  The  augmentation  of  the  transmitted  sound 
may  be  observed  simultaneously  with  the  generation  and 
brightening  of  the  colors  which  indicate  the  increasing 


326  SOUND. 

thinness  of  the  film.     A  very  thin  collodion-film  acts  in 
the  same  way. 

Acquainted  with  the  foregoing  facts  regarding  the  pas- 
sage of  sound  through  cambric,  silk, 'lint,  flannel,  baize, 
felt,  and  cotton-net,  you  are  prepared  for  the  statement 
that  the  sound-waves  pass  without  sensible  impediment 
through  heavy  artificial  showers  of  rain,  hail,  and  snow. 
Water-drops,  seeds,  sand,  bran,  and  flocculi  of  various 
kinds,  have  been  employed  to  form  such  showers;  through 
all  of  these,  as  through  the  actual  rain  and  hail  already  de- 
scribed, and  through  the  snow  on  the  Her  de  Glace,  the 
sound  passes  without  sensible  obstruction. 

§  4.  Action  of  Fog.     Observations  in  London. 

But  the  mariner's  greatest  ^enemy,  fog,  is  still  to  be 
dealt  with ;  and  here  for  a  long  time  the  proper  conditions 
of  experiment  were  absent.  Up  to  the  end  of  November 
we  had  had  frequent  days  of  haze,  sufficiently  thick  to  ob- 
scure the  white  cliffs  of  the  Foreland,  but  no  real  fog. 
Still  those  cases  furnished  demonstrative  evidence  that  the 
notions  entertained  regarding  the  reflection  of  sound  by 
suspended  particles  were  wrong;  for  on  many  days  of  the 
thickest  haze  the  sound  covered  twice  the  range  attained  on 
other  days  of  perfect  optical  transparency.  Such  instances 
dissolved  the  association  hitherto  assumed  to  exist  between 
acoustic  transparency  and  optic  transparency,  but  they  left 
the  action  of  dense  fogs  undetermined. 

On  December  9th  a  memorable  fog  settled  down  on 
London.  I  addressed  a  telegram  to  the  Trinity  House 
suggesting  some  gun  observations.  With  characteristic 
promptness  came  the  reply  that  they  would  be  made  in 
the  afternoon  at  Blackwall.  I  went  to  Greenwich  in  the 
hope  of  hearing  the  guns  across  the  river;  but  the  delay 
of  the  train  by  the  fog  rendered  my  arrival  too  late.  Over 
the  river  the  fog  was  very  dense,  and  through  it  came 


ACTION  OF  FOG.  327 

various  sounds  with  great  distinctness.  The  signal-bell  of 
an  unseen  barge  rang  clearly  out  at  intervals,  and  I  could 
plainly  hear  the  hammering  at  Cubitt's  Town,  half  a  mile 
away,  on  the  opposite  side  of  the  river.  No  deadening  of 
the  sound  by  the  fog  was  apparent. 

Through  this  fog  and  various  local  noises,  Captain  At- 
kins and  Mr.  Edwards  heard  the  report  of  a  12-pounder 
carronade  with  a  1-lb.  charge  distinctly  better  than  the 
18-pounder  with  a  3-lb.  charge,  an  optically  clear  atmos- 
phere, and  all  noise  absent,  on  July  3d. 

Anxious  to  turn  to  the  best  account  a  phenomenon  for 
which  we  had  waited  so  long,  I  tried  to  grapple  with  the 
problem  by  experiments  on  a  small  scale.  On  the  10th,  I 
stationed  my  assistant  with  a  whistle  and  organ-pipe  on 
the  walk  below  the  southwest  end  of  the  bridge  dividing 
Hyde  Park  from  Kensington  Gardens.  From  the  eastern 
end  of  the  Serpentine  I  heard  distinctly  both  the  whistle 
and  the  pipe,  which  produced  380  waves  a  second.  On 
changing  places  with  my  assistant,  I  heard  for  a  time 
the  distinct  blasts  of  the  whistle  only.  The  deeper  note 
of  the  organ-pipe  at  length  reached  me,  rising  sometimes 
to  great  distinctness,  and  sometimes  falling  to  inaudi- 
bility. The  whistle  showed  the  same  intermittence  as  to 
period,  but  in  an  opposite  sense;  for,  when  the  whistle 
was  faint,  the  pipe  was  strong,  and  vice  versa.  To  obtain 
the  fundamental  note  of  the  pipe,  it  had  to  be  blown 
gently,  and  on  the  whole  the  whistle  proved  the  most 
efficient  in  piercing  the  fog. 

An  extraordinary  amount  of  sound  filled  the  air  during 
these  experiments.  The  resonant  roar  of  the  Bayswater 
and  Knightsbridge  roads;  the  clangor  of  the  great  bell 
of  Westminster;  the  railway-whistles,  which  were  fre- 
quently blown,  and  the  fog-signals  exploded  at  the  various 
metropolitan  stations,  were  all  heard  with  extraordinary 
intensity.  This  could  by  no  means  be  reconciled  with  the 


328  SOUND. 

statements  so  categorically  made  regarding  the  acoustic 
impenetrability  of  a  London  fog. 

On  the  llth  of  December,  the  fog  being  denser  than 
before,  I  heard  every  blast  of  the  whistle,  and  occasional 
blasts  of  the  pipe,  over  the  distance  between  the  bridge 
and  the  eastern  end  of  the  Serpentine.  On  joining  my 
assistant  at  the  bridge,  the  loud  concussion  of  a  gun  was 
heard  by  both  of  us.  A  police-inspector  affirmed  that  it 
came  from  Woolwich,  and  that  he  had  heard  several  shots 
about  2  p.  M.  and  previously.  The  fact,  if  a  fact,  was  of 
the  highest  importance;  so  I  immediately  telegraphed  to 
"Woolwich  for  information.  Prof.  Abel  kindly  furnished 
me  with  the  following  particulars: 

"  The  firing  took  place  at  1.40  p.  M.  The  guns  proved 
were  of  comparatively  small  size — 64-pounders,  with  10-lb. 
charges  of  powder. 

"  The  concussion  experienced  at  my  house  and  office, 
about  three-quarters  of  a  mile  from  the  butt,  was  decidedly 
more  severe  than  that  experienced  when  the  heaviest  guns 
are  proved  with  charges  of  110  to  120  Ibs.  of  powder. 
There  was  a  dense  fog  here  at  the  time  of  firing." 

These  were  the  guns  heard  by  the  police-inspector;  on 
subsequent  inquiry  it  was  ascertained  that  two  guns  were 
fired  about  3  P.  M.  These  were  the  guns  heard  by  myself. 

Prof.  Abel  also  communicated  to  me  the  following 
fact :  "  Our  workman's  bell  at  the  Arsenal  Gate,  which  is 
of  moderate  size  and  anything  but  clear  in  tone,  is  pretty 
distinctly  heard  by  Prof.  Bloxam  only  when  the  wind 
is  northeast.  During  the  whole  of  last  week  the  bell 
was  heard  with  great  distinctness,  the  wind  being  south- 
westerly (opposed  to  the  sound).  The  distance  of  the  bell 
from  Bloxam's  house  is  about  three-quarters  of  a  mile  as 
the  crow  flies." 

Assuredly  no  question  of  science  ever  stood  so  much 
in  need  of  revision  as  this  of  the  transmission  of  sound 


OBSERVATIONS  IN  HYDE  PARK.  329 

through  the  atmosphere.  Slowly,  but  surely,  we  mastered 
the  question;  and  the  further  we  advanced,  the  more 
plainly  it  appeared  that  our  reputed  knowledge  regarding 
it  was  erroneous  from  beginning  to  end. 

On  the  morning  of  the  12th  the  fog  attained  its  maxi- 
mum density.  It  was  not  possible  to  read  at  my  window, 
which  fronted  the  open  western  sky.  At  10.30  I  sent  an 
assistant  to  the  bridge,  and  listened  for  his  whistle  and 
pipe  at  the  eastern  end  of  the  Serpentine.  The  whistle 
rose  to  a  shrillness  far  surpassing  anything  previously 
heard,  but  it  sank  sometimes  almost  to  inaudibility; 
proving  that,  though  the  air  was  on  the  whole  highly 
homogeneous,  acoustic  clouds  still  drifted  through  the  fog. 
A  second  pipe,  which  was  quite  inaudible  yesterday,  was 
plainly  heard  this  morning.  We  were  able  to  discourse 
across  the  Serpentine  to-day  with  much  greater  ease  than 
yesterday. 

During  our  summer  observations  I  had  once  or  twice 
been  able  to  fix  the  position  of  the  Foreland  in  thick  haze 
by  the  direction  of  the  sound.  To-day  my  assistant,  hid- 
den by  the  fog,  walked  up  to  the  Watermen's  Boat-house 
sounding  his  whistle;  and  I  walked  along  the  opposite  side 
of  the  Serpentine,  clearly  appreciating  for  a  time  that  the 
line  joining  us  was  oblique  to  the  axis  of  the  river.  'Com- 
ing to  a  point  which  seemed  to  be  exactly  abreast  of  him, 
I  marked  it;  and  on  the  following  day,  when  the  fog  had 
cleared  away,  the  marked  position  was  found  to  be  per- 
fectly exact.  When  undisturbed  by  echoes,  the  ear,  with 
a  little  practice,  becomes  capable  of  fixing  with  great  pre- 
cision the  direction  of  a  sound. 

On  reaching  the  Serpentine  this  morning,  a  peal  of 
bells,  which  then  began  to  ring,  seemed  so  close  at  hand 
that  it  required  some  reflection  to  convince  me  that  they 
were  ringing  to  the  north  of  Hyde  Park.  The  sounds 
fluctuated  wonderfully  in  power.  Prior  to  the  striking  of 


330  SOUND. 

eleven  by  the  great  bell  of  Westminster,  a  nearer  bell 
struck  with  loud  clangor.  The  first  five  strokes  of  the 
Westminster  bell  were  afterward  heard,  one  of  them  being 
extremely  loud;  but  the  last  six  strokes  were  inaudible. 
An  assistant  was  stationed  to  attend  to  the  12  o'clock  bells. 
The  clock  which  had  struck  so  loudly  at  11  was  unheard 
at  12,  while  of  the  Westminster  bell  eight  strokes  out  of 
twelve  were  inaudible.  To  such  astonishing  changes  is  the 
atmosphere  liable. 

At  7  P.  M.  the  Westminster  bell,  striking  seven,  was  not 
at  all  heard  from  the  Serpentine,  while  the  nearer  bell 
already  alluded  to  was  heard  distinctly.  The  fog  had 
cleared  away,  and  the  lamps  on  the  bridge  could  be  seen 
from  the  eastern  end  of  the  Serpentine  burning  brightly; 
but,  instead  of  the  sound  sharing  the  improvement  of  the 
light,  but  might  be  properly  called  an  acoustic  fog  took 
the  place  of  its  optical  predecessor.  Several  series  of 
the  whistle  and  organ-pipe  were  sounded  in  succession; 
one  series  only  of  the  whistle-sounds  was  heard,  all  the 
others  being  quite  inaudible.  Three  series  of  the  organ- 
pipe  were  heard,  but  exceedingly  faintly.  On  reversing 
the  positions  and  sounding  as  before,  nothing  whatever 
was  heard. 

At  8  o'clock  the  chimes  and  hour-bell  of  the  Westmin- 
ster clock  were  both  very  loud.  The  "  acoustic  fog  "  had 
shifted  its  position,  or  temporarily  melted  away. 

Extraordinary  fluctuations  were  also  observed  in  the 
case  of  the  church-bells  heard  in  the  morning:  in  a  few 
seconds  they  would  sink  from  a  loudly-ringing  peal  into 
utter  silence,  from  which  they  would  rapidly  return  to 
loud-tongued  audibility.  The  intermittent  drifting  of  fog 
over  the  sun's  disk  (by  which  his  light  is  at  times  obscured, 
at  times  revealed)  is  the  optical  analogue  of  these  effects. 
As  regards  such  changes,  the  acoustic  deportment  of  the 
atmosphere  is  a  true  transcript  of  its  optical  deportment. 


FLUCTUATION  OF  BELLS.  331 

At  9  P.  M.  three  strokes  only  of  the  Westminster  clock 
were  heard;  the  others  were  inaudible.  The  air  had  re- 
lapsed in  part  into  its  condition  at  7  P.  M.,  when  all  the 
strokes  were  unheard.  The  quiet  of  the  park  this  even- 
ing, as  contrasted  with  the  resonant  roar  which  filled  the 
air  on  the  two  preceding  days,  was  very  remarkable.  The 
sound,  in  fact,  was  stifled  in  the  optically  clear  but  acous- 
tically flocculent  atmosphere. 

On  the  13th,  the  fog  being  displaced  by  thin  haze,  I 
went  again  to  the  Serpentine.  The  carriage-sounds  were 
damped  to  an  extraordinary  degree.  The  roar  of  the 
Knightsbridge  and  Bayswater  roads  had  subsided,  the 
tread  of  troops  which  passed  us  a  little  way  off  was  un- 
heard, while  at  11  A.  M.  both  the  chimes  and  the  hour-bell 
of  the  Westminster  clock  were  stifled.  Subjectively  con- 
sidered, all  was  favorable  to  auditory  impressions;  but  the 
very  cause  that  damped  the  local  noises  extinguished  our 
experimental  sounds.  The  voice  across  the  Serpentine 
to-day,  with  my  assistant  plainly  visible  in  front  of  me, 
was  distinctly  feebler  than  it  had  been  when  each  of  us 
was  hidden  from  the  other  in  the  densest  fog. 

Placing  the  source  of  sound  at  the  eastern  end  of  the 
Serpentine  I  walked  along  its  edge  from  the  bridge  toward 
the  end.  The  distance  between  these  two  points  is  about 
1,000  paces.  After  500  of  them  had  been  stepped,  the 
sound  was  not  so  distinct  as  it  had  been  at  the  bridge  on 
the  day  of  densest  fog;  hence,  by  the  law  of  inverse 
squares,  the  optical  cleansing  of  the  air  through  the  melt- 
ing away  of  the  fog  had  so  darkened  it  acoustically,  that  a 
sound  generated  at  the  eastern  end  of  the  Serpentine  was 
lowered  to  one-fourth  of  its  intensity  at  a  point  midway 
between  the  end  and  the  bridge. 

To  these  demonstrative  observations  one  or  two  sub- 
sequent ones  may  be  added.  On  several  of  the  moist  and 
warm  days,  at  the  beginning  of  1874,  I  stood  at  noon 


332  SOUND. 

beside  the  railing  of  St.  James's  Park,  near  Buckingham 
Palace,  three-quarters  of  a  mile  from  the  clock-tower, 
which  was  clearly  visible.  oSTot  a  single  stroke  of  "  Big 
Ben  "  was  heard.  On  January  19th  fog  and  drizzling 
rain  obscured  the  tower;  still  from  the  same  position  I  not 
only  heard  the  strokes  of  the  great  bell,  but  also  the 
chimes  of  the  quarter-bells. 

During  the  exceedingly  dense  and  "  dripping  "  fog  of 
January  22d,  from  the  same  railings,  I  heard  every  stroke 
of  the  bell.  At  the  end  of  the  Serpentine,  when  the  fog 
was  densest,  the  Westminster  bell  was  heard  striking  loud- 
ly eleven.  Toward  evening  this  fog  began  to  melt  away, 
and  at  6  o'clock  I  went  to  the  end  of  the  Serpentine  to 
observe  the  effect  of  the  optical  clearing  upon  the  sound. 
Not  one  of  the  strokes  reached  me.  At  9  o'clock  and  at 
10  o'clock  my  assistant  was  in  the  same  position,  and  on 
both  occasions  he  failed  to  hear  a  single  stroke  of  the  bell. 
It  was  a  case  precisely  similar  to  that  of  December  13th, 
when  the  dissolution  of  the  fog  was  accompanied  by  a 
decided  acoustic  thickening  of  the  air.1 

§  5.  Observations  at  the  South  Foreland. 

Satisfactory,  and  indeed  conclusive,  as  these  results 
seemed,  I  desired  exceedingly  to  confirm  them  by  experi- 
ments with  the  instruments  actually  employed  at  the 
South  Foreland.  On  the  10th  of  February  I  had  the 
gratification  of  receiving  the  following  note  and  inclosure 
from  the  Deputy  Master  of  Trinity  House: 

"  MY  DEAR  TYNDALL:  The  inclosed  will  show  how 
accurately  your  views  have  been  verified,  and  I  send  them 
on  at  once  without  waiting  for  the  details.  I  think  you 

1  A  friend  informs  me  that  he  has  followed  a  pack  of  hounds  on  a 
clear  calm  day  without  hearing  a  single  yelp  from  the  dogs ;  while  on 
calm  foggy  days  from  the  same  distance  the  musical  uproar  of  the  pack 
was  loudly  audible. 


FOG-SIGNALS  IN  FOGS.  333 

will  be  glad  to  have  them,  and  as  soon  as  I  get  the  report 
it  shall  be  sent  to  you.  I  made  up  my  mind  ten  days  ago 
that  there  would  be  a  chance  in  the  light  foggy-disposed 
weather  at  home,  and  therefore  sent  the  Argus  off  at  an 
hour's  notice,  and  requested  the  Fog  Committee  to  keep 
one  member  on  board.  On  Friday  I  was  so  satisfied  that 
the  fog  would  occur  that  I  sent  Edwards  down  to  record 
the  observations. 

"  Very  truly  yours, 

"  FEED.  ARROW." 

The  inclosed  referred  to  was  notes  from  Captain  At- 
kins and  Mr.  Edwards.  Captain  Atkins  writes  thus: 

"  As  arranged,  I  came  down  here  by  the  mail  express, 
meeting  Mr.  Edwards  at  Cannon  Street.  We  put  up  at 
the  Dover  Castle,  and  next  morning  at  7  I  was  awoke  by 
sounds  of  the  siren.  On  jumping  up  I  discovered  that 
the  long-looked-for  fog  had  arrived,  and  that  the  Argus 
had  left  her  moorings. 

"  However,  had  I  been  on  board,  the  instructions  I  left 
with  Troughton  (the  master  of  the  Argus)  could  not  have 
been  better  carried  out.  About  noon  the  fog  cleared  up, 
and  the  Argus  returned  to  her  moorings,  when  I  learned 
that  they  had  taken  both  siren  and  horn  sounds  to  a  dis- 
tance of  11  miles  from  the  station,  where  they  dropped  a 
buoy.  This  I  knew  to  be  correct,  as  I  have  this  morning 
recovered  the  buoy,  and  the  distances  both  in  and  out 
agree  with  Troughton's  statement.  I  have  also  been  to 
the  Varne  light-ship  (12f  miles  from  the  Foreland),  and 
ascertained  that  during  the  fog  of  Saturday  forenoon  they 
'  distinctly  '  heard  the  sounds." 

Mr.  Edwards,  who  was  constantly  at  my  side  during 
our  summer  and  autumn  observations,  and  who  is  thor- 
oughly competent  to  form  a  comparative  estimate  of  the 
strength  of  the  sounds,  states  that  those  of  the  7th  were 


334  SOUND. 

"  extraordinarily  loud,"  both  Captain  Atkins  and  himself 
being  awoke  by  them.  He  does  not  remember  ever  before 
hearing  the  sounds  so  loud  in  Dover;  it  seemed  as  though 
the  observers  were  close  to  the  instruments. 

Other  days  of  fog  preceded  this  one,  and  they  were  all 
days  of  acoustic  transparency,  the  day  of  densest  fog  being 
acoustically  the  clearest  of  all. 

The  results  here  recorded  are  of  the  highest  impor- 
tance, for  they  bring  us  face  to  face  with  a  dense  fog  and 
an  actual  fog-signal,  and  confirm  in  the  most  conclusive 
manner  the  previous  observations.  The  fact  of  Captain 
Atkins  and  Mr.  Edwards  being  awakened  by  the  siren 
proves,  beyond  all  our  previous  experience,  its  power  dur- 
ing this  dense  fog. 

It  is  exceedingly  interesting  to  compare  the  transmis- 
sion of  sound  on  February  7th  with  its  transmission  on 
October  14th.  The  wind  on  both  days  had  the  same 
strength  and  direction.  My  notes  of  the  observations  show 
the  latter  to  have  been  throughout  a  day  of  extreme  opti- 
cal clearness.  The  range  was  10  miles.  During  the  fog 
of  February  7th  the  Argus  heard  the  sound  at  11  miles; 
and  it  was  also  heard  at  the  Varne  light-vessel,  which  is 
12f  miles  from  the  Foreland. 

It  is  also  worthy  of  note  that  through  the  same  fog  the 
sounds  were  well  heard  at  the  South  Sand  Head  light- 
vessel,  which  is  in  the  opposite  direction  from  the  South 
Foreland,  and  was  actually  behind  the  siren.  For  this 
important  circumstance  is  to  be  borne  in  mind :  on  Febru- 
ary 7th  the  siren  happened  to  be  pointed,  not  toward  the 
Argus,  but  toward  Dover.  Had  the  yacht  been  in  the 
axis  of  the  instrument  it  is  highly  probable  that  the 
sound  would  have  been  heard  all  the  way  across  to  the 
coast  of  France. 

It  is  hardly  necessary  for  me  to  say  a  word  to  guard 
myself  against  the  misconception  that  I  consider  sound 


FOG  AT  THE  SOUTH  FORELAND.  335 

to  be  assisted  by  the  fog  itself.  The  fog-particles  have  no 
more  influence  upon  the  waves  of  sourid  than  the  sus- 
pended particles  stirred  up  over  the  banks  of  Newfound- 
land have  upon  the  waves  of  the  Atlantic.  An  homogene- 
ous air  is  the  usual  associate  of  fog,  and  hence  the  acoustic 
clearness  of  foggy  weather. 

§  6.  Experiments  on  Artificial  Fogs. 

These  observations  are  clinched  and  finished  by  being 
brought  within  the  range  of  laboratory  experiments.  Here 
we  shall  learn  incidentally  a  lesson  as  to  the  caution  re- 
quired from  an  experimenter. 

The  smoke  from  smouldering  brown  paper  was  allowed 
to  stream  upward  through  its  rectangular  apertures,  into 
the  tunnel  abed  (Fig.  146) ;  the  action  upon  the  sound- 
waves was  strong,  rendering  the  short  and  agitated  sensi- 
tive flame  fc  tall  and  quiescent. 

Air  first  passed  through  ammonia,  then  through  hydro- 
chloric acid,  and,  thus  loaded  with  thick  fumes,  was  sent 
into  the  tunnel;  the  agitated  flame  was  rendered  imme- 
diately quiescent,  indicating  a  very  decided  action  on  the 
part  of  the  artificial  fog. 

Air  passed  through  perchloride  of  tin  and  sent  into 
the  tunnel  produced  exceedingly  dense  fumes.  The  action 
upon  the  sound-waves  was  very  strong. 

The  dense  smoke  of  resin,  burnt  before  the  open  end 
of  the  tunnel,  and  blown  into  it  with  a  pair  of  bellows,  had 
also  the  effect  of  stopping  the  sound-waves,  so  as  to  still 
the  agitated  flame. 

The  conclusion  seems  clear,  and  its  perfect  harmony 
with  the  prevalent  a  priori  notions  as  to  the  action  of  fog 
upon  sound  makes  it  almost  irresistible.  But  caution  is 
here  necessary.  The  smoke  of  the  brown  paper  was  hot; 
the  flask  containing  the  hydrochloride  acid  was  hot;  that 
containing  the  perchloride  of  tin  was  hot;  while  the  resin- 


336  SOUND. 

fumes  produced  by  a  red-hot  poker  were  also  obviously 
hot.  Were  the  results,  then,  due  to  the  fumes  or  to  the 
differences  of  temperature?  The  observations  might  well 
have  proved  a  trap  to  an  incautious  reasoner. 

Instead  of  the  smoke  and  heated  air,  the  heated  air 
alone  from  four  red-hot  pokers  was  permitted  to  stream  up- 
ward into  the  tunnel;  the  action  on  the  sound-waves  was 
very  decided,  though  the  tunnel  was  optically  empty.  The 
flame  of  a  candle  was  placed  at  the  upper  end,  and  the 
hot  air  just  above  its  tip  was  blown  into  the  tunnel;  the 
action  on  the  sensitive  flame  was  decided.  A  similar 
effect  was  produced  when  the  air,  ascending  from  a  red- 
hot  iron,  was  blown  into  the  tunnel. 

In  these  latter  cases  the  tunnel  remained  optically 
clear,  while  the  same  effect  as  that  produced  by  the  resin, 
smoke,  and  fumes,  was  observed.  Clearly,  then,  we  are 
not  entitled  to  ascribe,  without  further  investigation,  to 
the  artificial  fog  an  effect  which  may  have  been  due  to  the 
air  which  accompanied  it. 

Having  eliminated  the  fog  and  proved  the  non-homo- 
geneous air  effective,  our  reasoning  will  be  completed  by 
eliminating  the  heat,  and  proving  the  fog  ineffective. 

Instead  of  the  tunnel  abed,  Fig.  146,  a  cupboard 
with  glass  sides,  3  feet  long,  2  feet  wide,  and  about  5  feet 
high,  was  filled  with  fumes  of  various  kinds.  Here  it  was 
thought  the  fumes  might  remain  long  enough  for  differ- 
ences of  temperature  to  disappear.  Two  apertures  were 
made  in  two  opposite  panes  of  glass  3  feet  asunder.  In 
front  of  one  aperture  was  placed  the  bell  in  its  padded  box, 
and  behind  the  other  aperture,  and  at  some  distance  from 
it,  the  sensitive  flame. 

Phosphorus  placed  in  a  cup  floating  on  water  was 
ignited  within  the  closed  cupboard.  The  fumes  were  so 
dense  that  considerably  less  than  the  three  feet  traversed 
by  the  sound  extinguished  totally  a  bright  candle-flame. 


ARTIFICIAL  FOGS.  337 

At  first  there  was  a  slight  action  upon  the  sound;  but 
this  rapidly  vanished,  the  flame  being  no  more  affected 
than  if  the  sound  had  passed  through  pure  air.  The  first 
action  was  manifestly  due  to  differences  of  temperature, 
and  it  disappeared  when  the  temperature  was  equalized. 

The  cupboard  was  next  filled  with  the  dense  fumes  of 
gunpowder.  At  first  there  was  a  slight  action;  but  this 
disappeared  even  more  rapidly  than  in  the  case  of  the 
phosphorus,  the  sound  passing  as  if  no  fumes  were  there. 
It  required  less  than  half  a  minute  to  abolish  the  action 
in  the  case  of  the  phosphorus,  but  a  few  seconds  sufficed 
in  the  case  of  the  gunpowder.  These  fumes  were  far 
more  than  sufficient  to  quench  the  candle-flame. 

The  dense  smoke  of  resin,  when  the  temperature  had 
become  equable,  exerted  no  action  on  the  sound. 

The  fumes  of  gum-mastic  were  equally  ineffectual. 

The  fumes  of  the  perchloride  of  tin,  though  of  ex- 
traordinary density,  exerted  no  sensible  effect  upon  the 
sound. 

Exceedingly  dense  fumes  of  chloride  of  ammonium 
next  filled  the  cupboard.  A  fraction  of  the  length  of  the 
3-foot  tube  sufficed  to  quench  the  candle-flame.  Soon 
after  the  cupboard  was  filled,  the  sound  passed  without 
the  least  sensible  deterioration.  An  aperture  at  the  top 
of  the  cupboard  was  opened;  but  though  a  dense  smoke- 
column  ascended  through  it,  many  minutes  elapsed  before 
the  candle-flame  could  be  seen  through  the  attenuated 
fog. 

Steam  from  a  copper  boiler  was  so  copiously  admitted 
into  the  cupboard  as  to  fill  it  with  a  dense  cloud.  ~No  real 
cloud  was  ever  so  dense;  still  the  sound  passed  through  it 
without  the  least  sensible  diminution.  This  being  the 
case,  cloud-echoes  are  not  a  likely  phenomenon. 

In  all  of  these  cases,  when  a  couple  of  Bunsen's  burn- 
ers were  ignited  within  the  cupboard  continuing  the 


338  SOUND. 

fumes,  less  than  a  minute's  action  rendered  the  air  so 
heterogeneous  that  the  sensitive  flame  was  completely 
stilled. 

These  acoustically  inactive  fogs  were  subsequently 
proved  competent  to  cut  off  the  electric  light. 

Experiment  and  observation  go,  therefore,  hand  in 
hand  in  demonstrating  that  fogs  have  no  sensible  action 
upon  sound.  The  notion  of  their  impenetrability,  which 
so  powerfully  retarded  the  introduction  of  phonic  coast- 
signals,  being  thus  abolished,  we  have  solid  ground  for  the 
hope  that  disasters  due  to  fogs  and  thick  weather  will  in 
the  future  be  materially  mitigated. 

§  7.  Action  of  Wind. 

In  stormy  weather  we  were  frequently  forsaken  by  our 
steamer,  which  had  to  seek  shelter  in  the  Downs  or  Mar- 
gate Roads,  and  on  such  occasions  the  opportunity  was 
turned  to  account  to  determine  the  effect  of  the  wind. 
On  October  llth,  accompanied  by  Mr.  Douglass  and  Mr. 
Edwards,  I  walked  along  the  cliffs  from  Dover  Castle  to- 
ward the  Foreland,  the  wind  blowing  strongly  against  the 
sound.  About  a  mile  and  a  half  from  the  Foreland,  we 
first  heard  the  faint  but  distinct  sound  of  the  siren.  The 
horn-sound  was  inaudible.  A  gun  fired  during  our  halt 
was  also  unheard. 

As  we  approached  the  Foreland  we  saw  the  smoke  of 
a  gun.  Mr.  Edwards  heard  a  faint  crack,  but  neither 
Mr.  Douglass  nor  I  heard  anything.  The  sound  of  the 
siren  was  at  the  same  time  of  piercing  intensity.  We 
waited  for  ten  minutes,  when  another  gun  was  fired.  The 
smoke  was  at  hand,  and  I  thought  I  heard  a  faint  thud, 
but  could  not  be  certain.  My  companions  heard  nothing. 
On  pacing  the  distance  afterward  we  were  found  to  be 
only  550  yards  from  the  gun.  We  were  shaded  at  the 
time  by  a  slight  eminence  from  both  the  siren  and  the 


ACTION  OF  WIND.  339 

gun,  but  this  could  not  account  for  the  utter  extinction 
of  the  gun-sound  at  so  short  a  distance,  and  at  a  time  when 
the  siren  sent  to  us  a  note  of  great  power. 

Mr.  Ayres  at  my  request  walked  to  windward  along 
the  cliff,  while  Mr.  Douglass  proceeded  to  St.  Margaret's 
Bay.  During  their  absence  I  had  three  guns  fired.  Mr. 
Ayres  heard  only  one  of  them.  Favored  by  the  wind,  Mr. 
Douglass,  at  twice  the  distance,  and  far  more  deeply  im- 
mersed in  the  sound-shadow,  heard  all  three  reports  with 
the  utmost  distinctness. 

Joining  Mr.  Douglass,  we  continued  our  walk  to  a 
distance  of  three-quarters  of  a  mile  beyond  St.  Margaret's 
Bay.  Here,  being  dead  to  leeward,  though  the  wind  blew 
with  unabated  violence,  the  sound  of  the  siren  was  borne 
to  us  with  extraordinary  power.1  In  this  position  we  also 
heard  the  gun  loudly,  and  two  other  loud  reports  at  the 
proper  interval  of  ten  minutes,  as  we  returned  to  the 
Foreland. 

It  is  within  the  mark  to  say  that  the  gun  on  October 
llth  was  heard  five  times,  and  might  have  been  heard 
fifteen  times,  as  far  to  leeward  as  to  windward. 

In  windy  weather  the  shortness  of  its  sound  is  a  serious 
drawback  to  the  use  of  the  gun  as  a  signal.  In  the  case 
of  the  horn  and  siren,  time  is  given  for  the  attention  to 
be  fixed  upon  the  sound ;  and  a  single  puff,  while  cutting 
out  a  portion  of  the  blast,  does  not  obliterate  it  wholly. 
Such  a  puff,  however,  may  be  fatal  to  the  momentary 
gun-sound. 

On  the  leeward  side  of  the  Foreland,  on  the  23d  of 
October,  the  sounds  were  heard  at  least  four  times  as  far 
as  on  the  windward  side,  while  in  both  directions  the  siren 
possessed  the  greatest  penetrative  power. 

On  the  24th  the  wind  shifted  to  E.  S.  E.,  and  the 

1  The  horn  here  was  temporarily  suspended,  but  doubtless  would 
have  been  well  heard. 


340  SOUND. 

sounds,  which,  when  the  wind  was  W.  S.  W.  failed  to 
reach  Dover,  were  now  heard  in  the  streets  through  thick 
rain.  On  the  27th  the  wind  was  E.  N.  E.  In  our  writ- 
ing-room in  the  Lord  Warden  Hotel,  in  the  bedrooms,  and 
on  the  staircase,  the  sound  of  the  siren  reached  us  with  sur- 
prising power,  piercing  through  the  whistling  and  moaning 
of  the  wind,  which  blew  through  Dover  toward  Folkestone. 
The  sounds  were  heard  by  Mr.  Edwards  and  myself  at  6 
miles  from  the  Foreland  on  the  Folkestone  road;  and  had 
the  instruments  not  then  ceased  sounding,  they  might  have 
been  heard  much  farther.  At  the  South  Sand  Head 
light-vessel,  3|  miles  on- the  opposite  side,  no  sound  had 
been  heard  throughout  the  day.  On  the  28th,  the  wind 
being  N.  by  E.,  the  sounds  were  heard  in  the  middle  of 
Folkestone,  8  miles  off,  while  in  the  opposite  direction 
they  failed  to  reach  3f  miles.  On  the  29th  the  limits  of 
range  were  Eastware  Bay  on  the  one  side,  and  Kingsdown 
on  the  other;  on  the  30th  the  limits  were  Kingsdown  on 
the  one  hand,  and  Folkestone  Pier  on  the  other.  With  a 
wind  having  a  force  of  4  or  5  it  was  a  very  common  obser- 
vation to  hear  the  sound  in  one  direction  three  times  as 
far  as  in  the  other. 

This  well-known  effect  of  the  wind  is  exceedingly 
difficult  to  explain.  Indeed,  the/only  explanation  worthy 
of  the  name  is  one  offered  by  Prof.  Stokes,  and  sug- 
gested by  some  remarkable  observations  of  De  la  Roche. 
In  vol.  i.  of  "  Annales  de  Chimie  "  for  1816,  p.  176, 
Arago  introduces  De  la  Roche's  memoir  in  these  words: 
"  L'auteur  arrive  a  des  conclusions,  qui  d'abord  pourront 
paraitre  paradoxales,  mais  ceux  qui  savant  combien  il  met- 
tait  de  soins  et  d'exactitude  dans  toutes  ses  recherches  se 
garderont  sans  doute  d'opposer  une  opinion  populaire  a 
des  experiences  positives."  The  strangeness  of  De  la 
Roche's  results  consisted  in  his  establishing,  by  quantita- 
tive measurements,  not  only  that  sound  has  a  greater 


STOKES'S  EXPLANATION.  341 

range  in  the  direction  of  the  wind  than  in  the  opposite 
direction,  but  that  the  range  at  right  angles  to  the  wind  is 
the  maximum. 

In  a  short  but  exceedingly  able  communication,  pre- 
sented to  the  British  Association  in  1857,  the  eminent 
physicist  above  mentioned  points  out  a  cause  which,  if 
sufficient,  would  account  for  the  results  referred  to.  The 
lower  atmospheric  strata  are  retarded  by  friction  against 
the  earth,  and  the  upper  ones  by  those  immediately  below 
them;  the  velocity  of  transition,  therefore,  in  the  case  of 
wind,  increases  from  the  ground  upward.  It  may  be 
proved  that  this  difference  of  velocity  tilts  the  sound-wave 
upward  in  a  direction  opposed  to,  and  downward  in  a 
direction  coincident  with,  the  wind.  In  this  latter  case 
the  direct  wave  is  reenforced  by  the  wave  reflected  from 
the  earth.  Now  the  ree'nf  orcement  is  greatest  in  the  direc- 
tion in  which  the  direct  and  reflected  waves  inclose  the 
smallest  angle;  and  this  is  at  right  angles  to  the  direction 
of  the  wind.  Hence  the  greater  range  in  this  direction. 
It  is  not,  therefore,  according  to  Prof.  Stokes,  a  stifling  of 
the  sound  to  windward,  but  a  tilting  of  the  sound-wave 
over  the  heads  of  the  observers,  that  defeats  the  propaga- 
tion in  that  direction. 

This  explanation  calls  for  verification,  and  I  wished 
much  to  test  it  by  means  of  a  captive  balloon  rising  high 
enough  to  catch  the  deflected  wave;  but  on  communi- 
cating with  Mr.  Coxwell,  who  has  earned  for  himself  so 
high  a  reputation  as  an  aeronaut,  and  who  has  always 
shown  himself  so  willing  to  promote  a  scientific  object,  I 
learned  with  regret  that  the  experiment  was  too  dangerous 
to  be  carried  out.1 

1  Experiments  so  important  as  those  of  De  la  Roche  ought  not  to  be 
left  without  verification.  I  have  made  arrangements  with  a  view  to 
this  object. 


342  SOUND. 

§  8.  Atmospheric  Selection. 

It  has  been  stated  that  the  atmosphere  on  different 
days  shows  preferences  to  different  sounds.  This  point  is 
worthy  of  further  illustration. 

After  the  violent  shower  which  passed  over  us  on 
October  18th,  the  sounds  of  all  the  instruments,  as  already 
stated,  rose  in  power;  but  it  was  noticed  that  the  horn- 
sound,  which  was  of  lower  pitch  than  that  of  the  siren, 
improved  most,  at  times  not  only  equalling,  but  surpass- 
ing, the  sound  of  its  rival.  From  this  it  might  be  inferred 
that  the  atmospheric  change  produced  by  the  rain  favored 
more  especially  the  transmission  of  the  longer  sonorous 
waves. 

But  our  programme  enabled  us  to  go  further  than 
mere  inference.  It  had  been  arranged  on  the  day  men- 
tioned, that  up  to  3.30  p.  M.  the  siren  should  perform  2,400 
revolutions  a  minute,  generating  480  waves  a  second.  As 
long  as  this  rate  continued,  the  horn,  after  the  shower,  had 
the  advantage.  The  rate  of  rotation  was  then  changed  to 
2,000  a  minute,  or  400  waves  a  second,  when  the  siren- 
sound  immediately  surpassed  that  of  the  horn.  A  clear 
connection  was  thus  established  between  aerial  reflection 
and  the  length  of  the  sonorous  waves. 

The  10-inch  Canadian  whistle  being  capable  of  ad- 
justment so  as  to  produce  sounds  of  different  pitch,  on 
the  10th  of  October  I  ran  through  a  series  of  its  sounds. 
The  shrillest  appeared  to  possess  great  intensity  and  pene- 
trative power.  The  belief  is  common  that  a  note  of  this 
character  (which  affects  so  powerfully,  and  even  painfully, 
an  observer  close  at  hand)  has  also  the  greatest  range. 
Mr.  A.  Gordon,  in  his  examination  before  the  Committee 
on  Lighthouses,  in  1845,  expressed  himself  thus:  "  When 
you  get  a  shrill  sound,  high  in  the  scale,  that  sound  is 
carried  much  farther  than  a  lower  note  in  the  scale."  I 


ATMOSPHERIC  SELECTION.  343 

have  heard  the  same  opinion  expressed  by  other  scientific 
men. 

On  the  14th  of  October  the  point  was  submitted  to  an 
experimental  test.  It  had  been  arranged  that  up  to  11.30 
A.  M.  the  Canadian  whistle,  which  had  been  heard  with 
such  piercing  intensity  on  the  10th,  should  sound  its  shrill- 
est note.  At  the  hour  just  mentioned  we  were  beside  the 
Varne  buoy,  7f  miles  from  the  Foreland.  The  siren,  as 
we  approached  the  buoy,  was  heard  through  the  paddle- 
noises;  the  horns  were  also  heard,  but  more  feebly  than 
the  siren.  We  paused  at  the  buoy  and  listened  for  the 
11.30  gun.  Its  boom  was  heard  by  all.  Neither  before 
nor  during  the  pause  was  the  shrill-sounding  Canadian 
whistle  once  heard.  At  the  appointed  time  it  was  adjusted 
to  produce  its  ordinary  low-pitched  note,  which  was  im- 
mediately heard.  Farther  out  the  low  boom  of  the  cannon 
continued  audible  after  all  the  other  sounds  had  ceased. 

But  it  was  only  during  the  early  part  of  the  day  that 
this  preference  for  the  longer  wave  was  manifested.  At 
3  P.  M.  the  case  was  completely  altered,  for  then  the  high- 
pitched  siren  was  heard  when  all  the  other  sounds  were  in- 
audible. On  many  other  days  we  had  illustrations  of  the 
varying  comparative  power  of  the  siren  and  the  gun. 
On  the  9th  of  October  sometimes  the  one,  sometimes  the 
other,  was  predominant.  On  the  morning  of  the  13th  the 
siren  was  clearly  heard  on  Shakespeare's  Cliff,  while 
two  guns  with  their  puffs  perfectly  visible  were  unheard. 
On  October  16,  2  miles  from  the  signal  station,  the  gun  at 
11  o'clock  was  inferior  to  the  siren,  but  both  were  heard. 
At  12.30,  the  distance  being  6  miles,  the  gun  was  quite 
unheard,  while  the  siren  continued  faintly  audible.  Later 
on  in  the  day  the  experiment  was  twice  repeated.  The 
puff  of  the  gun  was  in  each  case  seen,  but  nothing  was 
heard.  In  the  last  experiment,  when  the  gun  was 
quenched,  the  siren  sent  forth  a  sound  so  strong  as  to  main- 


344  SOUND. 

tain  itself  through  the  paddle-noises.  The  day  was  clearly 
hostile  to  the  passage  of  the  longer  sonorous  waves. 

October  17th  began  with  a  preference  for  the  shorter 
waves.  At  11.30  A.  M.  the  mastery  of  the  siren  over  the 
gun  was  pronounced;  at  12.30  the  gun  slightly  surpassed 
the  siren;  at  1,  2,  and  2.30  p.  M.  the  gun  also  asserted  its 
mastery.  This  preference  for  the  longer  waves  was  con- 
tinued on  October  18th.  On  October  20th  the  day  began 
in  favor  of  the  gun,  then  both  became  equal,  and  finally  the 
siren  gained  the  mastery;  but  the  day  had  become  stormy, 
and  a  storm  is  always  unfavorable  to  the  momentary  gun- 
sound.  The  same  remarks  applies  to  the  experiments  of 
October  21st.  At  11  A.  M.,  distance  6^  miles,  when  the 
siren  made  itself  heard  through  the  noises  of  wind,  sea, 
and  paddles,  the  gun  was  fired;  but,  though  listened  for 
with  all  attention,  no  sound  was  heard.  Half  an  hour 
later  the  result  was  the  same.  On  October  24th  five  ob- 
servers saw  the  flash  of  the  gun  at  a  distance  of  5  miles, 
but  heard  nothing;  all  of  them  at  this  distance  heard  the 
siren  distinctly;  a  second  experiment  on  the  same  day 
yielded  the  same  result.  On  the  27th  also  the  siren  was 
triumphant;  and  on  three  several  occasions  on  the  29th 
its  mastery  over  the  gun  was  very  decided. 

Such  experiments  yield  new  conceptions  as  to  the  scat- 
tering of  sound  in  the  atmosphere.  Xo  sound  here  em- 
ployed is  a  simple  sound;  in  every  case  the  fundamental 
note  is  accompanied  by  others,  and  the  action  of  the  at- 
mosphere on  these  different  groups  of  waves  has  its  optical 
analogue  in  that  scattering  of  the  waves  of  the  luminif- 
erous  ether  which  produces  the  various  shades  and  colors 
of  the  sky. 

§  9.  Concluding  Remarks. 

A  few  additional  remarks  and  suggestions  will  fitly 
wind  up  this  chapter.  It  has  been  proved  that  in  some 


DISADVANTAGES  OF  GUN.  345 

states  of  the  weather  the  howitzer  firing  a  3-lb.  charge 
commands  a  larger  range  than  the  whistles,  trumpets,  or 
siren.  This  was  the  case,  for  example,  on  the  particular 
day,  October  17th,  when  the  ranges  of  all  the  sounds 
reached  their  maximum. 

On  many  other  days,  however,  the  inferiority  of  the 
gun  to  the  siren  was  demonstrated  in  the  clearest  manner. 
The  gun-puffs  were  seen  with  the  utmost  distinctness  at 
the  Foreland,  but  no  sound  was  heard,  the  note  of  the  siren 
at  the  same  time  reaching  us  with  distinct  and  consider- 
able power. 

The  disadvantages  of  the  gun  are  these: 

a.  The  duration  of  the  sound  is  so  short  that,  unless 
the  observer  is  prepared  beforehand,  the  sound,  through 
lack  of  attention  rather  than  through  its  own  powerless- 
ness,  is  liable  to  be  unheard. 

•b.  Its  liability  to  be  quenched  by  the  local  sound  is  so 
great,  that  it  is  sometimes  obliterated  by  a  puff  of  wind 
taking  possession  of  the  ears  at  the  time  of  its  arrival. 
This  point  was  alluded  to  by  Arago,  in  his  report  on  the 
celebrated  experiments  of  1822.  By  such  a  puff  a  mo- 
mentary gap  is  produced  in  the  case  of  a  continuous  sound, 
but  not  entire  extinction. 

c.  Its  liability  to  be  quenched  or  deflected  by  an  oppos- 
ing wind,  so  as  to  be  practically  useless  at  a  very  short 
distance  to  windward,  is  very  remarkable.  A  case  has 
been  cited  in  which  the  gun  failed  to  be  heard  against  a 
violent  wind  at  a  distance  of  550  yards  from  the  place  of 
firing,  the  sound  of  the  siren  at  the  same  time  reaching  us 
with  great  intensity. 

Still,  notwithstanding  these  drawbacks,  I  think  the 
gun  is  entitled  to  rank  as  a  first-class  signal.  I  have  had 
occasion  myself  to  observe  its  extreme  utility  at  Holyhead 
and  the  Kish  light-vessel  near  Kingstown.  The  command- 
ers of  the  Holyhead  boats,  moreover,  are  unanimous  in 


316  SOUND. 

their  commendation  of  the  gun.  An  important  addition 
in  its  favor  is  the  fact  that  in  a  fog  the  flash  or  glare  often 
comes  to  the  aid  of  the  sound.  On  this  point,  the  evi- 
dence is  quite  conclusive. 

There  may  be  cases  in  which  the  combination  of  the 
gun  with  one  of  the  other  signals  may  be  desirable. 
Where  it  is  wished  to  confer  an  unmistakable  individual- 
ity on  a  fog-signal  station,  such  a  combination  might  with 
advantage  be  resorted  to. 

If  the  gun  be  retained  as  one  form  of  fog-signal  (and 
I  should  be  sorry  at  present  to  recommend  its  total  abo- 
lition), it  ought  to  be  of  the  most  suitable  description. 
Our  experiments  prove  the  sound  of  the  gun  to  be  depend- 
ent on  its  shape;  but  we  do  not  know  that  we  have  em- 
ployed the  -best  shape.  This  suggests  the  desirability  of 
constructing  a  gun  with  special  reference  to  the  production 
of  sound.1 

An  absolutely  uniform  superiority  on  all  days  cannot 
be  conceded  to  any  one  of  the  instruments  subjected  to 
examination;  still,  our  observations  have  been  so  numer- 
ous and  long-continued  as  to  enable  us  to  come  to  the  sure 
conclusion  that,  on  the  whole,  the  steam-siren  is  the  most 
powerful  fog-signal  which  has  hitherto  been  tried  in  Eng- 
land. It  is  specially  powerful  when  local  noises,  such  as 
those  of  wind,  rigging,  breaking  waves,  shore-surf,  and 
the  rattle  of  pebbles,  have  to  be  overcome.  Its  den- 
sity, quality,  pitch,  and  penetration,  render  it  dominant 
over  such  noises  after  all  other  signal-sounds  have  suc- 
cumbed. 

I  have  not,  therefore,  hesitated  to  recommend  the  in- 
troduction of  the  siren  as  a  coast-signal. 

It  will  be  desirable  in  each  case  to  confer  upon  the 
instrument  a  power  of  rotation,  so  as  to  enable  the  person 

1  The  Elder  Brethren  have  already  had  plans  of  a  new  signal-gun 
laid  before  them  by  the  constructors  of  the  War  Department. 


MINIMUM  RANGE  OF  FOG-SIGNALS.  347 

in  charge  of  it  to  point  its  trumpet  against  the  wind  or  in 
any  other  required  direction.  This  arrangement  was  made 
at  the  South  Foreland,  and  it  presents  no  mechanical  dif- 
ficulty. It  is  also  desirable  to  mount  the  siren,  so  as  to 
permit  of  the  depression  of  its  trumpet  fifteen  or  twenty 
degrees  below  the  horizon. 

In  selecting  the  position,  at  which  a  fog-signal  is  to  be 
mounted,  the  possible  influence  of  a  sound-shadow,  and 
the  possible  extinction  of  the  sound  by  the  interference  of 
the  direct  waves  with  waves  reflected  from  the  shore, 
must  form  the  subject  of  the  gravest  consideration.  Pre- 
liminary trials  may,  in  most  cases,  be  necessary  before 
fixing  on  the  precise  point  at  which  the  instrument  is  to 
be  placed. 

The  siren  which  has  been  long  known  to  scientific  men 
is  worked  with  air;  and  it  would  be  worth  while  to  try 
how  the  fog-siren  would  behave  supposing  compressed  air 
to  be  substituted  for  steam.  Compressed  air  might  also 
be  tried  with  the  whistles. 

!No  fog-signal  hitherto  tried  is  able  to  fulfill  the  condi- 
tion laid  down  in  a  very  able  letter  already  referred  to, 
namely,  "  that  all  fog-signals  should  be  distinctly  audible 
for  at  least  4  miles  under  every  circumstance."  Circum- 
stances may  exist  to  prevent  the  most  powerful  sound  from 
being  heard  at  half  this  distance.  What  may  with  cer- 
tainty be  affirmed,  is  that  in  almost  all  cases  the  siren  may 
certainly  be  relied  on  at  a  distance  of  2  miles;  in  the  great 
majority  of  cases  it  may  be  relied  upon  at  a  distance  of  3 
miles,  and  in  the  majority  of  cases  to  a  distance  greater 
than  3  miles. 

Happily  the  experiments  thus  far  made  are  perfectly 
concurrent  in  indicating  that  at  the  particular  time  when 
fog-signals  are  needed,  the  air  holding  the  fog  in  sus- 
pension is  in  a  highly-homogeneous  condition ;  hence  it  is  in 
the  highest  degree  probable  that  in  the  case  of  fog  we  may 


348  SOUND. 

rely  upon  the  signals  being  effective  at  far  greater  dis- 
tances than  those  just  mentioned. 

I  am  cautious  not  to  inspire  the  mariner  with  a  confi- 
dence which  may  prove  delusive.  When  he  hears  a  fog- 
signal  he  ought,  as  a  general  rule  (at  all  events  until  ex- 
tended experience  justifies  the  contrary),  to  assume  the 
source  of  sound  to  be  not  more  than  2  or  3  miles  distant, 
and  to  heave  his  lead  or  to  take  other  necessary  precau- 
tions. If  he  errs  at  all  in  his  estimate  of  distance,  it 
ought  to  be  on  the  side  of  safety. 

With  the  instruments  now  at  our  disposal  wisely  estab- 
lished along  coasts,  I  venture  to  think  that  the  saving  of 
property  in  ten  years  will  be  an  exceedingly  large  mul- 
tiple of  the  outlay  necessary  for  the  establishment  of  such 
signals.  The  saving  of  life  appeals  to  the  higher  motives 
of  humanity. 

In  a  report  written  for  the  Trinity  House  on  the  sub- 
ject of  fog-signals,  my  excellent  predecessor,  Prof.  Fara- 
day, expresses  the  opinion  that  a  false  promise  to  the 
mariner  would  be  worse  than  no  promise  at  all.  Casting 
our  eyes  back  upon  the  observations  here  recorded,  we 
find  the  sound-range  on  clear,  calm  days  varying  from  2| 
miles  to  16£  miles.  It  must  be  evident  that  an  instruc- 
tion founded  on  the  latter  observation  would  be  fraught 
with  peril  in  weather  corresponding  to  the  former. 
Not  the  maximum  but  the  minimum  sound-range  should 
be  impressed  upon  the  mariner.  Want  of  atten- 
tion to  this  point  may  be  followed  by  disastrous  conse- 
quences. 

This  remark  is  not  made  without  cause.  I  have 
before  me  a  "  Notice  to  Mariners  "  regarding  a  fog-whistle 
recently  mounted  at  Cape  Race,  which  is  reputed  to  have 
a  range  of  20  miles  in  calm  weather,  30  miles  with  the 
wind,  and  in  stormy  weather  or  against  the  wind  7  to  10 
miles.  Now,  considering  the  distance  reached  by  sound 


CONCLUSION.  349 

in  our  observations,  I  should  be  willing  to  concede  the 
possibility,  in  a  more  homogeneous  atmosphere  than  ours, 
of  a  sound-range  on  some  calm  days  of  20  miles,  and  on 
some  light  windy  days  of  30  miles,  to  a  powerful  whistle; 
but  I  entertain  a  strong  belief  that  the  stating  of  these 
distances,  or  of  the  distance  7  to  10  miles  against  a  storm, 
without  any  qualification,  is  calculated  to  inspire  the 
mariner  with  false  confidence.  I  would  venture  to  affirm 
that  at  Cape  Race  calm  days  might  be  found  in  which  the 
range  of  the  sound  will  be  less  than  one-fourth  of  what 
this  notice  states  it  to  be.  Such  publications  ought  to  be 
without  a  trace  of  exaggeration,  and  furnish  only  data  on 
which  the  mariner  may  with  perfect  confidence  rely.  My 
object  in  extending  these  observations  over  so  long  a  period 
was  to  make  evident  to  all  how  fallacious  it  would  be,  and 
how  mischievous  it  might  be,  to  draw  general  conclusions 
from  observations  made  in  weather  of  great  acoustic  trans- 
parency. 

Thus  ends,  for  the  present  at  all  events,  an  inquiry 
which  I  trust  will  prove  of  some  importance,  scientific  as 
well  as  practical.  In  conducting  it  I  have  had  to  congrat- 
ulate myself  on  the  unfailing  aid  and  cooperation  of  the 
Elder  Brethren  of  the  Trinity  House.  Captain  Drew, 
Captain  Close,  Captain  Were,  Captain  Atkins,  and  the 
Deputy  Master,  have  all  from  time  to  time  taken  part  in 
the  inquiry.  To  the  eminent  arctic  navigator,  Admiral 
Collinson,  who  showed  throughout  unflagging  and,  I  would 
add,  philosophic  interest  in  the  investigation,  I  am  in- 
debted for  most  important  practical  aid.  He  was  almost 
always  at  my  side,  comparing  opinions  with  me,  placing 
the  steamer  in  the  required  positions,  and  making  with 
consummate  skill  and  promptness  the  necessary  sextant  ob- 
servations. I  am  also  deeply  sensible  of  the  important 
services  rendered  by  Mr.  Douglass,  the  able  and  indefatiga- 
ble engineer,  by  Mr.  Ayres,  the  assistant  engineer,  and  by 


350  SOUND. 

Mr.  Price  Edwards,  the  private  secretary  of  the  Deputy 
Master  of  the  Trinity  House. 

The  officers  and  gunners  at  the  South  Foreland  also 
merit  my  best  thanks,  as  also  Mr.  Holmes  and  Mr.  Laid- 
law,  who  had  charge  of  the  trumpets,  whistles,  and 
siren. 

In  the  subsequent  experimental  treatment  of  the  sub- 
ject I  have  been  most  ably  aided  by  my  excellent  assistant, 
Mr.  John  Cottrell. 


NOTE. 

In  the  Appendix  will  be  found  a  brief  paper  on  "  Acoustic  Reversi- 
bility," in  which  I  offer  a  solution  of  a  difficulty  encountered  by  the 
French  philosophers  in  their  experiments  on  the  velocity  of  sound  in 
1822.  The  solution  is  based  on  the  experiments  and  observations  re- 
corded in  the  foregoing  chapter. — J.  T. 


SUMMARY.  351 


SUMMARY  OF  CHAPTER  VII. 

THE  paper  of  Dr.  Derham,  published  in  the  "  Philo- 
sophical Transactions  "  for  1708,  has  been  hitherto  the  al- 
most exclusive  source  of  our  knowledge  of  the  causes  which 
affect  the  transmission  of  sound  through  the  atmosphere* 

Derham  found  that  fog  obstructed  sound,  that  rain 
and  hail  obstructed  sound,  but  that  above  all  things  falling 
snow,  or  a  coating  of  fresh  snow  upon  the  ground,  tended 
to  check  the  propagation  of  sound  through  the  atmosphere. 

With  a  view  to  the  protection  of  life  and  property  at 
sea  in  the  years  1873  and  1874,  this  subject  received  an 
exhaustive  examination,  observational  and  experimental. 
The  investigation  was  conducted  at  the  expense  of  the 
Government  and  under  the  auspices  of  the  Elder  Breth- 
ren of  Trinity  House. 

The  most  conflecting  results  were  at  first  obtained. 
On  the  19th  of  May,  1873,  the  sound  range  was  3£  miles; 
on  the  20th  it  was  5^  miles;  on  the  2d  of  June,  6  miles; 
on  the  3d,  more  than  9  miles;  on  the  10th,  9  miles;  on 
the  25th,  6  miles;  on  the  26th,  9|  miles;  on  the  1st  of 
July,  12f  miles;  on  the  2d,  4  miles;  while  on  the  3d, 
with  a  clear  calm,  atmosphere  and  smooth  sea,  it  was  less 
than  3  miles. 

These  discrepancies  were  proved  to  be  due  to  a  state 
of  the  air  which  bears  the  same  relation  to  sound  that 
cloudiness  does  to  light.  By  streams  of  air  differently 
heated,  or  saturated  in  different  degrees  with  aqueous 
vapors,  the  atmosphere  is  rendered  flocculent  to  sound. 

Acoustic  clouds,  in  fact,  are  incessantly  floating  or 
2? 


352  SOUND. 

flying  through  the  air.  They  have  nothing  whatever  to 
do  with  ordinary  clouds,  fogs,  or  haze.  The  most  trans- 
parent atmosphere  may  be  filled  with  them;  converting 
days  of  extraordinary  optical  transparency  into  days  of 
equally  extraordinary  acoustic  opacity. 

The  connection  hitherto  supposed  to  exist  between  a 
clear  atmosphere  and  the  transmission  of  sound  is  there- 
fore dissolved. 

The  intercepted  sound  is  wasted  by  repeated  reflections 
in  the  acoustic  cloud,  as  light  is  wasted  by  repeated  re- 
flections in  an  ordinary  cloud.  And  as  from  the  ordinary 
cloud  the  light  reflected  reaches  the  eye,  so  from  the  per- 
fectly invisible  acoustic  cloud  the  reflected  sound  reaches 
the  ear. 

Aerial  echoes  of  extraordinary  intensity,  and  of  long 
duration  are  thus  produced.  They  occur,  contrary  to  the 
opinion  hitherto  entertained,  in  the  clearest  air. 

It  is  to  the  wafting  of  such  acoustic  clouds  through 
the  atmosphere  that  the  fluctuations  in  the  sounds  of  our 
public  clocks  and  of  church-bells  are  due. 

The  existence  of  these  aerial  echoes  has  been  proved 
both  by  observation  and  experiment.  They  may  arise 
either  from  air-currents  differently  heated,  or  from  air- 
currents  differently  saturated  with  vapor. 

Rain  has  no  sensible  power  to  obstruct  sound. 

Hail  has  no  sensible  power  to  obstruct  sound. 

Snow  has  no  sensible  power  to  obstruct  sound. 

Fog  has  no  sensible  power  to  obstruct  sound. 

The  air  associated  with  fog  is,  as  a  general  rule,  highly 
homogeneous  and  favorable  to  the  transmission  of  sound. 
The  notions  hitherto  entertained  regarding  the  action  of 
fog  are  untenable. 

Experiments  on  artificial  showers  of  rain,  hail,  and 
snow,  and  on  artificial  fogs  of  extraordinary  density,  con- 
firm the  results  of  observation. 


SUMMARY.  353 

As  long  as  the  air  forms  a  continuous  medium  the 
amount  of  sound  scattered  by  small  bodies  suspended  in  it 
is  astonishingly  small. 

This  is  illustrated  by  the  ease  with  which  sound  trav- 
erses layers  of  calico,  cambric,  silk,  flannel,  baize,  and  felt. 
It  freely  passes  through  all  these  substances  in  thicknesses 
sufficient  to  intercept  the  light  of  the  sun. 

Through  six  layers  of  thin  silk,  for  example,  it  passes 
with  little  obstruction;  it  finds  its  way  through  a  layer 
of  close  felt  half  an  inch  thick,  and  it  is  not  wholly  inter- 
cepted by  200  layers  of  cotton-net. 

The  atmosphere  exercises  a  selective  choice  upon  the 
waves  of  sound  which  varies  from  day  to  day,  and  even 
from  hour  to  hour.  It  is  sometimes  favorable  to  the  trans- 
mission of  the  longer,  and  at  other  times  favorable  to  the 
transmission  of  the  shorter,  sonorous  waves. 

The  recognized  action  of  the  wind  has  been  confirmed 
by  this  investigation. 


CHAPTER  VIII. 

Law  of  Vibratory  Motions  in  Water  and  Air. — Superposition  of  Vibra- 
tions.— Interference  of  Sonorous  Waves. — Destruction  of  Sound  by 
Sound. — Combined  Action  of  Two  Sounds  nearly  in  Unison  with 
each  other.— Theory  of  Beats. — Optical  Illustration  of  the  Principle 
of  Interference. — Augmentation  of  Intensity  by  Partial  Extinction 
of  Vibrations. — Resultant  Tones. — Conditions  of  their  Production. 
— Experimental  Illustrations. — Difference-Tones  and  Summation- 
Tones.— Theories  of  Young  and  Helmholtz. 

§  1.  Interference  of  Water -Waves. 

FROM  a  boat  in  Cowes  Harbor,  in  moderate  weather,  I 
have  often  watched  the  masts  and  ropes  of  the  ships,  as 
mirrored  in  the  water.  The  images  of  the  ropes  revealed 
the  condition  of  the  surface,  indicating  by  long  and  wide 
protuberances  the  passage  of  the  larger  rollers,  and,  by 
smaller  indentations,  the  ripples  which  crept  like  parasites 
over  the  sides  of  the  larger  waves.  The  sea  was  able  to 
accommodate  itself  to  the  requirements  of  all  its  undula- 
tions, great  and  small.  When  the  surface  was  touched 
with  an  oar,  or  when  drops  were  permitted  to  fall  from 
the  oar  into  the  water,  there  was  also  room  for  the  tiny 
wavelets  thus  generated.  This  carving  of  the  surface  by 
waves  and  ripples  had  its  limit  only  in  my  powers  of  ob- 
servation; every  wave  and  every  ripple  asserted  its  right 
of  place,  and  retained  its  individual  existence,  amid  the 
crowd  of  other  motions  which  agitated  the  water. 

The  law  that  rules  this  chasing  of  the  sea,  this  crossing 
and  intermingling  of  innumerable  small  waves,  is  that  the 
resultant  motion  of  every  particle  of  water  is  the  sum  of 
354 


SUPERPOSITION  OF  VIBRATIONS.  355 

the  individual  motions  imparted  to  it.  If  a  particle  be 
acted  on  at  the  same  moment  by  two  impulses,  both  of 
which  tend  to  raise  it,  it  will  be  lifted  by  a  force  equal  to 
the  sum  of  both.  If  acted  upon  by  two  impulses,  one  of 
which  tends  to  raise  it,  and  the  other  to  depress  it,  it  will 
be  acted  upon  by  a  force  equal  to  the  difference  of  both. 
When,  therefore,  the  sum  of  the  motions  is  spoken  of,  the 
algebraic  sum  is  meant — the  motions  which  tend  to  raise 
the  particle  being  regarded  as  positive,  and  those  which 
tend  to  depress  it  as  negative. 

When  two  stones  are  cast  into  smooth  water,  20  or  30 
feet  apart,  round  each  stone  is  formed  a  series  of  expand- 
ing circular  waves,  every  one  of  which  consists  of  a  ridge 
and  a  furrow.  The  waves  touch,  cross  each  other,  and 
carve  the  surface  into  little  eminences  and  depressions. 
Where  ridge  coincides  with  ridge,  we  have  the  water  raised 
to  a  double  height;  where  furrow  coincides  with  furrow, 
we  have  it  depressed  to  a  double  depth;  where  ridge  coin- 
cides with  furrow,  we  have  the  water  reduced  to  its 
average  level.  The  resultant  motion  of  the  water  at  every 
point  is,  as  above  stated,  the  algebraic  sum  of  the  motions 
impressed  upon  that  point.  And  if,  instead  of  two  sources 
of  disturbance,  we  had  ten,  or  a  hundred,  or  a  thousand, 
the  consequence  would  be  the  same;  the  actual  result 
might  transcend  our  powers  of  observation,  but  the  law 
above  enunciated  would  still  hold  good. 

Instead  of  the  intersection  of  waves  from  two  distinct 
centres  of  disturbance,  we  may  cause  direct  and  reflected 
waves,  from  the  same  centre,  to  cross  each  other.  Many 
of  you  know  the  beauty  of  the  effects  produced  when  light 
is  reflected  from  ripples  of  water.  When  mercury  is 
employed  the  effect  is  more  brilliant  still.  Here,  by  a 
proper  mode  of  agitation,  direct  and  reflected  waves  may 
be  caused  to  cross  and  interlace,  and  by  the  most  wonder- 
ful self -analysis  to  untie  their  knotted  scrolls.  The  adja- 


356  SOUND. 

cent  figure  (Fig.  149),  which  is  copied  from  the  excellent 
"  Wellenlehre  "  of  the  brothers  Weber,  will  give  some 
idea  of  the  beauty  of  these  effects.  It  represents  the  chas- 

FIG.  149. 


ing  produced  by  the  intersection  of  direct  and  reflected 
water-waves  in  a  circular  vessel,  the  point  of  disturbance 
(marked  by  the  smallest  circle  in  the  figure)  being  midway 
between  the  centre  and  the  circumference. 

This  power  of  water  to  accept  and  transmit  multitu- 
dinous impulses  is  shared  by  air,  which  concedes  the  right 
of  space  and  motion  to  any  number  of  sonorous  waves. 
The  same  air  is  competent  to  accept  and  transmit  the 
vibrations  of  a  thousand  instruments  at  the  same  time. 
When  we  try  to  visualize  the  motion  of  that  air — to  pre- 
sent to  the  eye  of  the  mind  the  battling  of  the  pulses 
direct  and  reverberated — the  imagination  retires  baffled 
from  the  attempt.  Still,  amid  all  the  complexity,  the 


INTERFERENCE  OF  SOUND.  357 

law  above  enunciated  holds  good,  every  particle  of  air 
being  animated  by  the  resultant  motion,  which  is  the  alge- 
braic sum  of  all  the  individual  motions  imparted  to  it. 
And  the  most  wonderful  thing  of  all  is,  that  the  human 
ear,  though  acted  on  only  by  a  cylinder  of  that  air,  which 
does  not  exceed  the  thickness  of  a  quill,  can  detect  the 
components  of  the  motion,  and,  by  an  act  of  attention,  can 
even  isolate  from  the  aerial  entanglement  any  particular 
sound. 

§  2.  Interference  of  Sound. 

When  two  unisonant  tuning-forks  are  sounded  togeth- 
er, it  is  easy  to  see  that  the  forks  may  so  vibrate  that  the 
condensations  of  the  one  shall  coincide  with  the  conden- 
sations of  the  other,  and  the  rarefactions  of  the  one  with 
the  rarefactions  of  the  other.  If  this  be  the  case,  the  two 
forks  will  assist  each  other.  The  condensations  will,  in 
fact,  became  more  condensed,'  the  rarefactions  more  rare- 
fied; and  as  it  is  upon  the  difference  of  density  between 
the  condensations  and  rarefactions  that  loudness  depends, 
the  two  vibrating  forks,  thus  supporting  each  other,  will 
produce  a  sound  of  greater  intensity  than  that  of  either  of 
them  vibrating  alone. 

It  is,  however,  also  to  see  that  the  two  forks  may  be 
so  related  to  each  other  that  one  of  them  shall  require  a 
condensation  at  the  place  where  the  other  requires  a  rare- 
faction; that  the  one  fork  shall  urge  the  air-particles  for- 
ward, while  the  other  urges  them  backward.  If  the  op- 
posing forces  be  equal,  particles  so  solicited  will  move 
neither  backward  nor  forward,  the  aerial  rest  which  corre- 
sponds to  silence  being  the  result.  Thus,  it  is  possible,  by 
adding  the  sound  of  one  fork  to  that  of  another,  to  abolish 
the  sounds  of  both.  We  have  here  a  phenomenon  which, 
above  all  others,  characterizes  wave-motion.  It  was  this 
phenomenon,  as  manifested  in  optics,  that  led  to  the  undu- 


358  SOUND. 

latory  theory  of  light,  the  most  cogent  proof  of  that  theory 
being  based  upon  the  fact  that,  by  adding  light  to  light, 
we  may  produce  darkness,  just  as  we  can  produce  silence 
by  adding  sound  to  sound. 

During  the  vibration  of  a  tuning-fork  the  distance 
between  the  two  prongs  is  alternately  increased  and  dimin- 
ished. Let  us  call  the  motion  which  increases  the  distance 
the  outward  swing,  and  that  which  diminishes  the  dis- 
tance the  inward  swing  of  the  fork.  And  let  us  suppose 
that  our  two  forks,  A  and  B,  Fig.  150,  reach  the  limits 
of  their  outward  swing  and  their  inward  swing  at  the  same 
moment.  In  this  case  the  phases  of  their  motion,  to  use 
the  technical  term,  are  the  same.  For  the  sake  of  sim- 
plicity we  will  confine  our  attention  to  the  right-hand 
prongs,  A  and  B,  of  the  two  forks,  neglecting  the  other  two 


FIG.  150. 


prongs;  and  now  let  us  ask  what  must  be  the  distance 
between  the  prongs  A  and  B,  when  the  condensations  and 
rarefactions  of  both,  indicated  respectively  by  the  dark 
and  light  shading,  coincide?  A  little  reflection  will  make 
it  clear  that  if  the  distance  from  B  to  A  be  equal  to  the 
length  of  a  whole  sonorous  wave,  coincidence  between 
the  two  systems  of  waves  must  follow.  The  same  would 
evidently  occur  were  the  distance  between  A  and  B  two 
wave-lengths,  three  wave-lengths,  four  wave-lengths — in 
short,  any  number  of  whole  wave-lengths.  In  all  such 
cases  we  shall  have  coincidence  of  the  two  systems  of 
waves,  and  consequently  a  reinforcement  of  the  sound  of 
the  one  fork  by  that  of  the  other.  Both  the  condensa- 


REfiNFORCEMENT  OF  SOTJXD  BY  SOUND.          359 

tions  and  rarefactions  between  A  and  c  are,  in  this  case, 
more  pronounced  than  they  would  be  if  either  of  the  forks 
were  suppressed. 

But  if  the  prong  B  be  only  half  the  length  of  a  wave 
behind  A,  what  must  occur?  Manifestly  the  rarefactions 
of  one  of  the  systems  of  waves  will  then  coincide  with  the 
condensations  of  the  other  system,  the  air  to  the  right  of  A 
being  reduced  to  quiescence.  This  is  shown  in  Fig.  151, 

FIG.  151. 


where  the  uniformity  of  shading  indicates  an  absence  both 
of  condensations  and  rarefactions.  When  B  is  two  half 
wave-lengths  behind  A,  the  waves,  as  already  explained, 
support  each  other;  when  they  are  three  half  wave-lengths 
apart,  they  destroy  each  other.  Or,  expressed  generally, 
we  have  augmentation  or  destruction  according  as  the  dis- 
tance between  the  two  prongs  amounts  to  an  even  or  an 
odd  number  of  semi-undulations.  Precisely  the  same  is 
true  of  the  waves  of  light.  If  through  any  cause  one  sys- 
tem of  ethereal  waves  be  any  even  number  of  semi-undula- 
tions behind  another  system,  the  two  systems  support  each 
other  when  they  coalesce,  and  we  have  more  light.  If  the 
one  system  be  any  odd  number  of  semi-undulations  behind 
the  other,  they  oppose  each  other,  and  a  destruction  of 
light  is  the  result  of  their  coalescence. 

The  action  here  referred  to,  both  as  regards  sound  and 
light,  is  called  Interference. 


360  SOUND. 

§  3.  Experimental  Illustrations. 

Sir  John  Herschel  was  the  first  to  propose  to  divide  a 
stream  of  sound  into  two  branches,  of  different  lengths, 
causing  the  branches  afterward  to  reunite,  and  interfere 
with  each  other.  This  idea  has  been  recently  followed  out 
with  success  by  M.  Quincke;  and  it  has  been  still  further 
improved  upon  by  M.  Konig.  The  principle  of  these 
experiments  will  be  at  once  evident  from  Fig.  152.  The 

FIG.  152. 


tube  o  f  divides  into  two  branches  at  /,  the  one  branch 
being  carried  round  n,  and  the  other  round  m.  The  two 
branches  are  caused  to  reunite  at  g,  and  to  end  in  a  com- 
mon canal,  g  p.  The  portion  &  n  of  the  tube  which  slides 
over  a  &  can  be  drawn  out  as  shown  in  the  figure,  and 
thus  the  sound-waves  can  be  caused  to  pass  over  different 
distances  in  the  two  branches.  Placing  a  vibrating 
tuning-fork  at  o,  and  the  ear  at  p,  when  the  two  branches 
are  of  the  same  length,  the  waves  through  both  reach  the 
ear  together,  and  the  sound  of  the  fork  is  heard. 
Drawing  n  &  out,  a  point  is  at  length  obtained  where  the 
sound  of  the  fork  is  extinguished.  This  occurs  when  the 
distance  a  &  is  one-fourth  of  a  wave-length;  or,  in  other 
words,  when  the  whole  right-hand  branch  is  half  a  wave- 
length longer  than  the  left-hand  one.  Drawing  &  n  still 
farther  out,  the  sound  is  again  heard;  and  when  twice 


BEATS.  361 

the  distance  a  b  amounts  to  a  whole  wave-length,  it 
reaches  a  maximum.  Thus,  according  as  the  difference  of 
both  branches  amounts  to  half  a  wave-length,  or  to  a  whole 
wave-length,  we  have  reenf orcement  or  destruction  .of  the 
two  series  of  sonorous  waves.  In  practice,  the  tube  o  f 
ought  to  be  prolonged  until  the  direct  sound  of  the  fork 
is  unheard,  the  attention  of  the  ear  being  then  wholly  con- 
centrated on  the  sounds  that  reach  it  through  the  tube. 

It  is  quite  plain  that  the  wave-length  of  any  simple 
tone  may  be  readily  found  by  this  instrument.  It  is  only 
necessary  to  ascertain  the  difference  of  path  which  pro- 
duces complete  interference.  Twice  this  difference  is  the 
wave-length;  and  if  the  rate  of  vibration  be  at  the  same 
time  known,  we  can  immediately  calculate  the  velocity  of 
sound  in  air. 

Each  of  the  two  forks  now  before  you  executes  exactly 
256  vibrations  in  a  second.  Sounded  together,  they  are 
in  unison.  Loading  one  of  them  with  a  bit  of  wax,  it 
vibrates  a  little  more  slowly  than  its  neighbor.  The  wax, 
say,  reduces  the  number  of  vibrations  to  255  in  a  second; 
how  must  their  waves  affect  each  other?  If  they  start  at 
the  same  moment,  condensation  coinciding  with  condensa- 
tion, and  rarefaction  with  rarefaction,  it  is  quite  manifest 
that  this  state  of  things  cannot  continue.  At  the  128th 
vibration  their  phases  are  in  complete  opposition,  one  of 
them  having  gained  half  a  vibration  on  the  other.  Here 
the  one  fork  generates  a  condensation  where  the  other 
generates  a  rarefaction:  and  the  consequence  is,  that  the 
two  forks  at  this  particular  point,  completely  neutralize 
each  other.  From  this  point  onward,  however,  the  forks 
support  each  other  more  and  more,  until,  at  the  end  of  a 
second,  when  the  one  has  completed  its  255th,  and  the 
other  its  256th  vibration,  condensation  again  coincides 
with  condensation,  and  rarefaction  with  rarefaction,  the 
full  effect  of  both  sounds  being  produced  upon  the  ear. 


362  SOUND. 

It  is  quite  manifest  that  under  these  circumstances  we 
cannot  have  the  continuous  flow  of  perfect  unison.  We 
have  on  the  contrary,  alternate  reinforcements  and  dimi- 
nutions of  the  sound.  We  obtain,  in  fact,  the  effect 
known  to  musicians  by  the  name  of  beats,  which,  as  here 
explained,  are  a  result  of  interference. 

I  now  load  this  fork  still  more  heavily,  by  attaching  a 
fourpenny-piece  to  the  wax;  the  coincidences  and  interfer- 
ences follow  each  other  more  rapidly  than  before;  we 
have  a  quicker  succession  of  beats.  In  our  last  experi- 
ment, the  one  fork  accomplished  one  vibration  more  than 
the  other  in  a  second,  and  we  had  a  single  beat  in  the 
same  time.  In  the  present  case,  one  fork  vibrates  250 
times,  while  the  other  vibrates  256  times  in  a  second,  and 
the  number  of  beats  per  second  is  6.  A  little  reflection 
will  make  it  plain  that  in  the  interval  required  by  the 
one  fork  to  execute  one  vibration  more  than  the  other,  a 
beat  must  occur;  and  inasmuch  as,  in  the  case  now  before 
us,  there  are  six  such  intervals  in  a  second,  there  must  be 
six  beats  in  the  same  time.  In  short,  the  number  of  beats 
per  second  is  always  equal  to  the  difference  between  the 
two  rates  of  vibration. 

§  4.  Interference  of  Waves  from  Organ-pipes. 

Beats  may  be  produced  by  all  sonorous  bodies.  These 
two  tall  organ-pipes,  for  example,  when  sounded  together, 
give  powerful  beats,  one  of  them  being  slightly  longer 
than  the  other.  Here  are  two  other  pipes,  which  are  now 
in  perfect  unison,  being  exactly  of  the  same  length.  But 
it  is  only  necessary  to  bring  the  finger  near  the  embou- 
chure of  one  of  the  pipes,  Fig.  153,  to  lower  its  rate  of 
vibration,  and  produce  loud  and  rapid  beats.  The  placing 
of  the  hand  over  the  open  top  of  one  of  the  pipes  also 
lowers  its  rate  of  vibration,  and  produces  beats,  which  fol- 


MODES  OF  PRODUCING  BEATS. 


363 


low  each  other  with  augmented  rapidity  as  the  top  of  the 
pipe  is  closed  more  and  more.  By  a  stronger  blast  the 
first  two  harmonics  of  the  pipes  are  brought  out.  These 
higher  notes  also  interfere,  FIG.  153. 

and  you  have  these  quicker 
beats. 

Uo  more  beautiful  illus- 
tration of  this  phenomenon 
can  be  adduced  than  that 
furnished  by  two  sounding- 
flames.  Two  such  flames  are 
now  before  you,  the  tube  sur- 
rounding one  of  them  being 
provided  with  a  telescopic 
slider,  Fig.  154  (next  page). 
There  are,  at  present,  no 
beats,  because  the  tubes  are 
not  sufficiently  near  unison. 
I  gradually  lengthen  the 
shorter  tube  by  raising  its 
slider.  Eapid  beats  are 
now  heard;  now  they  are 
slower;  now  slower  still;  and  now  both  flames  sing  to- 
gether in  perfect  unison.  Continuing  the  upward  motion 
of  the  slider,  I  make  the  tube  too  long;  the  beats  begin 
again,  and  quicken,  until  finally  their  sequence  is  so 
rapid  as  to  appeal  only  as  roughness  to  the  ear.  The 
flames,  you  observe,  dance  within  their  tubes  in  time 
to  the  beats.  As  already  stated,  these  beats  cause  a 
silent  flame  within  a  tube  to  quiver  when  the  voice  is 
thrown  to  a  proper  pitch,  and  when  the  position  of 
the  flame  is  rightly  chosen,  the  beats  set  it  singing. 
With  the  flames  of  large  rose-burners,  and  with  tin  tubes 
from  3  to  9  feet  long,  we  obtain  beats  of  exceeding 
power. 


364:  SOUND. 

You  have  just  heard  the  beats  produced  by  two  tall 
organ-pipes  nearly  in  unison  with  each  other.     Two  other 

FIG.  154. 


pipes  are  now  mounted  on  our  wind-chest,  Fig.  155,  each 
of  which,  however,  is  provided  at  its  centre  with  a  mem- 
brane intended  to  act  on  the  flame.1  Two  small  tubes 
lead  from  the  spaces  closed  by  the  membranes,  and  unite 
afterward,  the  membranes  of  both  the  organ-pipes  being 
thus  connected  with  the  same  flame.  By  means  of  the 
sliders,  s,  s',  near  the  summit  of  the  pipes,  they  are  either 
brought  into  unison  or  thrown  out  of  it  at  pleasure.  They 
are  not  at  present  in  unison,  and  the  beats  they  produce 
follow  each  other  with  great  rapidity.  The  flame  con- 

1  Described  in  Chapter  V.,  p.  216. 


ACTION  OF  BEATS  ON  FLAME.  365 

nected  with  the  central  membranes  dances  in  time  to  the 
beats.     When  brought  nearer  to  unison,  the  beats  are 

FIG.  155. 


slower,  and  the  flame  at  successive  intervals  withdraws  its 
light  and  appears  to  exhale  it.  A  process  which  reminds 
you  of  the  inspiration  and  expiration  of  the  breath  is  thus 
carried  on  by  the  flame.  If  the  mirror,  M,  be  now  turned, 
the  flame  produces  a  luminous  band — continues  at  certain 
places,  but  for  the  most  part  broken  into  distinct  images 
of  the  flame.  The  continuous  parts  correspond  to  the 
intervals  of  interference  where  the  two  sets  of  vibrations 
abolish  each  other. 

Instead  of  permitting  both  pipes  to  act  upon  the  same 
flame,  we  may  associate  a  flame  with  each  of  them.  The 
deportment  of  the  flames  is  then  very  instructive.  Imag- 
ine both  flames  to  be  in  the  same  vertical  line,  the  one 


366  SOUND. 

of  them  being  exactly  under  the  other.  Bringing  the 
pipes  into  unison,  and  turning  the  mirror,  we  resolve  each 
flame  into  a  chain  of  images,  but  we  notice  that  the  im- 
ages of  the  one  occupy  the  spaces  between  the  images  of 
the  other.  The  periods  of  extinction  of  the  one  flame, 
therefore,  correspond  to  the  periods  of  kindling  of  the 
other.  The  experiment  proves  that,  when  two  unisonant 
pipes  are  placed  thus  close  to  each  other,  their  vibrations 
are  in  opposite  phases.  The  consequence  of  this  is,  that 
the  two  sets  of  vibrations  permanently  neutralize  each 
other,  so  that  at  a  little  distance  from  the  pipes  you  fail  to 
hear  the  fundamental  tone  of  either.  For  this  reason  we 
cannot,  with  any  advantage,  place  close  to  each  other  in  an 
organ  several  pipes  of  the  same  pitch.  . 


§    5.  Lissajous's  Illustration  of  Beats  of  Two  Tuning- 
forks. 

In  the  case  of  beats,  the  amplitude  of  the  oscillating 
air  reaches  a  maximum  and  a  minimum  periodically.  By 
the  beautiful  method  of  M.  Lissajous  we  can  illustrate 
optically  this  alternate  augmentation  and  diminution  of 
amplitude.  Placing  a  large  tuning-fork,  T',  Fig.  156,  in 
front  of  the  lamp  L,  a  luminous  beam  is  received  upon 
the  mirror  attached  to  the  fork.  This  is  reflected  back  to 
the  mirror  of  a  second  fork,  T,  and  by  it  thrown  on  to  the 
screen,  where  it  forms  a  luminous  disk.  When  the  bow  is 
drawn  over  the  fork  T',  the  beam,  as  in  the  experiments 
described  in  the  second  chapter,  is  tilted  up  and  down,  the 
disk  upon  the  screen  stretching  to  a  luminous  band  three 
feet  long.  If,  in  drawing  the  bow  over  this  second  fork, 
the  vibrations  of  both  coincide  in  phase,  the  band  will  be 
lengthened ;  if  the  phases  are  in  opposition,  total  or  partial 
neutralization  of  the  one  fork  by  the  other  will  be  the  re- 
sult. It  so  happens  that  in  the  present  instance  the  second 


OPTICAL  ILLUSTRATIONS  OF  BEATS. 


367 


fork  adds  something  to  the  action  of  the  first,  the  band  of 
light  being  now  four  feet  long.  These  forks  have  been 
tuned  as  perfectly  as  possible.  Each  of  them  executes  ex- 
actly 64  vibrations  in  a  second;  the  initial  relation  of  their 
phases  remains,  therefore,  constant,  and  hence  you  notice 
a  gradual  shortening  of  the  luminous  band,  like  that  ob- 

FIG.  156. 


served  during  the  subsidence  of  the  vibrations  of  a  single 
fork.  The  band  at  length  dwindles  to  the  original  disk, 
which  remains  motionless  upon  the  screen. 

By  attaching,  with  wax,  a  threepenny-piece  to  the 
prong  of  one  of  these  forks,  its  rate  of  vibration  is  lowered. 
The  phases  of  the  two  forks  cannot  now  retain  a  constant 
relation  to  each  other.  One  fork  incessantly  gains  upon 
the  other,  and  the  consequence  is  that  sometimes  the  phases 
of  both  coincide,  and  at  other  times  they  are  in  opposition. 
Observe  the  result.  At  the  present  moment  the  two  forks 
conspire,  and  we  have  a  luminous  band  four  feet  long  upon 
the  screen.  This  slowly  contracts,  drawing  itself  up  to  a 
mere  disk;  but  the  action  halts  here  only  during  the  mo- 
ment of  opposition.  That  passed,  the  forks  begin  again  to 
24 


368  SOUND. 

assist  each  other,  and  the  disk  once  more  slowly  stretches 
into  a  band.  The  action  here  is  very  slow;  but  it  may  be 
quickened  by  attaching  a  sixpence  to  the  loaded  fork. 
The  band  of  light  now  stretches,  and  contracts  in  perfect 
rhythm.  The  action,  rendered  thus  optically  evident,  is 
impressed  upon  the  air  of  this  room ;  its  particles  alternate- 
ly vibrate  and  come  to  rest,  and,  as  a  consequence,  beats 
are  heard  in  synchronism  with  the  changes  of  the  figure 
upon  the  screen. 

The  time  which  elapses  from  maximum  to  maximum, 
or  from  minimum  to  minimum,  is  that  required  for  the 
one  fork  to  perform  one  vibration  more  than  the  other. 
At  present  this  time  is  about  two  seconds.  In  two  seconds, 
therefore,  one  beat  occurs.  When  we  augment  the  disso- 
nance by  increasing  the  load,  the  rhythmic  lengthening 
and  shortening  of  the  band  is  more  rapid,  while  the  in- 
termittent hum  of  the  forks  is  more  audible.  There  are 
now  six  elongations  and  shortenings  in  the  interval  taken 
up  a  moment  ago  by  one;  the  beats  at  the  same  time  be- 
ing heard  at  the  rate  of  three  a  second.  By  loading  the 
fork  still  more,  the  alternations  may  be  caused  to  succeed 
each  other  so  rapidly  that  they  can  no  longer  be  followed 
by  the  eye,  while  the  beats,  at  the  same  time,  cease  to  be 
individually  distinct,  and  appeal  as  a  kind  of  roughness  to 
the  ear. 

In  the  experiments  with  a  single  tuning-fork,  already 
described  (Fig.  22,  Chapter  II.),  the  beam  reflected  from 
the  fork  was  received  on  a  looking-glass,  and,  by  turning 
the  glass,  the  band  of  light  on  the  screen  was  caused  to 
stretch  out  into  a  long  wavy  line.  It  was  explained  at  the 
time  that  the  loudness  of  the  sound  depended  on  the  depth 
of  the  indentations.  Hence,  if  the  band  of  light  of  vary- 
ing length  now  before  us  on  the  screen  be  drawn  out  in  a 
sinuous  line,  the  indentations  ought  to  be  at  some  places 
deep,  while  at  others  they  ought  to  vanish  altogether. 


EXPERIMENTS  OF  HOPKINS  AND  LISSAJOUS.     3G9 

This  is  the  case.  By  a  little  tact  the  mirror  of  the  fork  T 
(Fig.  156)  is  caused  to  turn  through  a  small  angle,  a  sinu- 
ous line  composed  of  swellings  and  contractions  (Fig.  157) 
being  drawn  upon  the  screen.  The  swellings  correspond 

FIG.  157. 


to  the  periods  of  sound,  and  the  contractions  to  those  of 
silence.1 

Two  vibrating  bodies,  then,  each  of  which  separately 
produces  a  musical  sound,  can,  when  acting  together, 
neutralize  each  other.  Hence,  by  quenching  the  vibra- 
tions of  one  of  them,  we  may  give  sonorous  effect  to  the 
other.  It  often  happens,  for  instance,  that  when  two 
tuning-forks,  on  their  resonant  cases,  are  vibrating  in 
unison,  the  stoppage  of  one  of  them  is  accompanied  by 
an  augmentation  of  the  sound.  This  point  may  be  further 
illustrated  by  the  vibrating  bell,  already  described  (Fig. 
78,  Chapter  IV.).  Placing  its  resonant  tube  in  front  of 
one  of  its  nodes,  a  sound  is  heard,  but  nothing  like  what  is 
heard  when  the  tube  is  opposed  to  a  ventral  segment.  The 
reason  of  this  is  that  the  vibrations  of  a  bell  on  the  oppo- 
site sides  of  a  nodal  line  are  in  opposite  directions,  and 
they  therefore  interfere  with  each  other.  By  introducing 
a  glass  plate  between  the  bell  and  the  tube,  the  vibrations 
on  one  side  of  the  nodal  line  may  be  intercepted;  an 
instant  augmentation  of  the  sound  is  the  consequence. 

1  The  figure  is  but  a  meagre  representation  of  the  fact.  The  band 
of  light  was  two  inches  wide,  the  depth  of  the  sinuosities  varying  from 
three  feet  to  zero. 


370 


SOUND. 


FIG.  158. 


§  6.  Interference  of  Waves  from  a  Vibrating  Disk. 
Hopkins' 's  and  Lissajous's  Illustrations. 

In  a  vibrating  disk  every  two  adjacent  sectors  move  at 
the  same  time  in  opposite  directions.  When  the  one 
sector  rises  the  other  falls,  the  nodal  line  marking  the 
limit  between  them.  Hence,  at  the  moment  when  any 
sector  produces  a  condensation  in  the  air  above  it,  the 
adjacent  sector  produces  a  rarefaction  in  the  same  air.  A 
partial  destruction  of  the  sound  of  one  sector  by  the  other 

is  the  result.  You  will 
now  understand  the  in- 
strument by  which  the 
late  William  Hopkins 
illustrated  the  principle 
of  interference.  The  tube 
A  B,  Fig.  15 8, divides  at  B 
into  two  branches.  The 
end  A  of  the  tube  is 
closed  by  a  membrane. 
Scattering  sand  upon  this 
membrane,  and  holding 
the  ends  of  the  branches 
over  adjacent  sectors  of 
a  vibrating  disk,  no  mo- 
tion (or,  at  least,  an  extremely  feeble  motion)  of  the  sand 
is  perceived.  Placing  the  ends  of  the  two  branches  over 
alternate  sectors  of  the  disk,  the  sand  is  tossed  from  the 
membrane,  proving  that  in  this  case  we  have  coincidence 
of  vibration  on  the  part  of  the  two  sectors. 

We  are  now  prepared  for  a  very  instructive  experi- 
ment, which  we  owe  to  M.  Lissajous.  Drawing  a  bow 
over  the  edge  of  a  brass  disk,  I  divide  it  into  six  vibrat- 
ing sectors.  When  the  palm  of  the  hand  is  brought 
over  any  one  of  them,  the  sound,  instead  of  being  di- 


INTENSITY  AUGMENTED  BY  PARTIAL  EXTINCTION.    371 

minished,  is  augmented.  When  two  hands  are  placed 
over  two  adjacent  sectors,  you  notice  no  increase  of 
the  sound;  but  when  they  are  placed  over  alternate 
sectors,  as  in  Fig.  159,  a  striking  augmentation  of  the 
sound  is  the  consequence.  ^^  FIG.  159. 

By  simply  lowering  and 
raising  the  hands,  marked 
variations  of  intensity  are 
produced.  By  the  approach 
of  the  hands  the  vibrations 
of  the  two  sectors  are  in- 
tercepted; their  interfer- 
ence right  and  left  being 
thus  abolished,  the  remain- 
ing sectors  sound  more 
loudly.  Passing  the  single 
hand  to  and  fro  along  the 
surface,  you  also  hear  a  rise 
and  fall  of  the  sound.  It  rises  when  the  hand  is  over  a 
vibrating  sector;  it  falls  when  the  hand  is  over  a  nodal 
line.  Thus  by  sacrificing  a  portion  of  the  vibrations,  we 
make  the  residue  more  effectual.  Experiments  similar  to 
these  may  be  made  with  light  and  radiant  heat.  If  of 
two  beams  of  the  former,  which  destroy  each  other  by 
interference,  one  be  removed,  light  takes  the  place  of 
darkness;  and  if  of  two  interfering  beams  of  the  latter 
one  be  intercepted,  heat  takes  the  place  of  cold. 


§  7.  Quenching  the  Sound  of  one  Prong  of  a  Tuning- 
fork  by  that  of  the  other. 

You  have  remarked  the  almost  total  absence  of  sound 
on  the  part  of  a  vibrating  tuning-fork  when  held  free  in 
the  hand.  The  feebleness  of  the  fork  as  a  sounding  body 
arises  in  part  from  interference.  The  prongs  always  vi- 


372  SOUND. 

brate  in  opposite  directions,  one  producing  a  condensation 
where  the  other  produces  a  rarefaction,  a  destruction  of 
sound  being  the  consequence.  By  simply  passing  a  paste- 
board tube  over  one  of  the  prongs  of  the  fork,  its  vibrations 
are  in  part  intercepted,  and  an  augmentation  of  the  sound 
is  the  result.  The  single  prong  is  thus  proved  to  be  more 
effectual  than  the  two  prongs.  There  are  positions  in 
which  the  destruction  of  the  sound  of  one  prong  by  that 
of  the  other  is  total.  These  positions  are  easily  found  by 
FIG.  160.  striking  the  fork 

and  turning  it 
round  before  the 
ear.  When  the 
back  of  the  prong 
is  parallel  to  the 

j HHHHypTl  ear,  the  sound  is 

"""""    tjKi  heard;  when  the 

side   surfaces   of 
both  prongs  are 
parallel    to    the 
ear,  the  sound  is 
\          also  heard;    but 
when  the  corner 
of  a  prong  is  carefully  presented  to  the  ear,  the  sound  is 
utterly  destroyed.     During  one  complete  rotation  of  the 
fork  we  find  four  positions  where  the  sound  is  thus. ob- 
literated. 

Let  s  s  (Fig.  160)  represent  the  two  ends  of  the  tun- 
ing-fork, looked  down  upon  it  as  it  stands  upright.  When 
the  ear  is  placed  at  a  or  &,  or  at  c  or  d,  the  sound  is  heard. 
Along  the  four  dotted  lines,  on  the  contrary,  the  waves 
generated  by  the  two  prongs  completely  neutralize  each 
other,  and  nothing  is  there  heard.  These  lines  have  been 
proved  by  Weber  to  be  hyperbolic  curves ;  and  this  must  be 
their  character  according  to  the  principle  of  interference. 


INTERFERENCE  OP  WAVES  OF  TUNING-FORK.      373 


FIG.  161. 


This  remarkable  case  of  interference,  which  was  first 
noticed  by  Dr.  Thomas  Young,  and  thoroughly  investi- 
gated by  the  brothers  Weber,  may  be  rendered  audible 
by  means  of  resonance.  Bringing  a  vibrating  fork  over 
a  jar  which  resounds  to  it,  and  causing  the  fork  to  ro- 
tate slowly,  in  four  positions  we  have  a  loud  resonance; 
in  four  others  absolute  silence,  alternate  risings  and  fall- 
ings of  the  sound  accompanying  the  fork's  rotation.  While 
the  fork  is  over  the  jar  with  its  corner  downward  and 
the  sound  entirely  extinguished,  let  a  pasteboard  tube  be 
passed  over  one  of  its  prongs,  as  in  Fig.  161,  a  loud 
resonance  announces 
the  withdrawal  of 
the  vibrations  of 
that  prong.  To  ob- 
tain this  effect,  the 
fork  must  be  held 
over  the  centre  of 
the  jar,  so  that  the 
aid  shall  be  symmet- 
rically distributed  on 
both  sides  of  it.  Mov- 
ing the  fork  from 
the  centre  toward 
one  of  the  sides,  without  altering  its  inclination  in  the 
least,  we  obtain  a  forcible  sound.  Interference,  however, 
is  also  possible  near  the  side  of  the  jar.  Holding  the 
fork,  not  with  its  corner  downward,  but  with  both  its 
prongs  in  the  same  horizontal  plane,  a  position  is  soon 
found  near  the  side  of  the  jar  where  the  sound  is  extin- 
guished. In  passing  completely  from  side  to  side  over 
the  mouth  of  the  jar,  two  such  places  of  interference  are 
discoverable. 

A  variety  of  experiments  will  suggest  themselves  to 
the  reflecting  mind,  by  which  the  effect  of  interference 


37±  SOUND. 

may  be  illustrated.  It  is  easy,  for  example,  to  find  a  jar 
which  resounds  to  a  vibrating  plate.  Such  a  jar,  placed 
over  a  vibrating  segment  of  the  plate,  produces  a  powerful 
resonance.  Placed  over  a  nodal  line,  the  resonance  is 
entirely  absent;  but  if  a  piece  of  pasteboard  be  interposed 
between  the  jar  and  plate,  so  as  to  cut  off  the  vibrations 
on  one  side  of  the  nodal  line,  the  jar  instantly  resounds 
to  the  vibrations  of  the  other.  Again,  holding  two  forks, 
which  vibrate  with  the  same  rapidity,  over  two  resonant 
jars,  the  sound  of  both  flows  forth  in  unison.  When  a 
bit  of  wax  is  attached  to  one  of  the  forks,  powerful  beats 
are  heard.  Removing  the  wax,  the  unison  is  restored. 
When  one  of  these  unisonant  forks  is  placed  in  the  flame 
of  a  spirit-lamp  its  elasticity  is  changed,  and  it  produces 

FIG.  162. 


long  loud  beats  with  its  unwarmed  fellow.1  If  while  one 
of  the  forks  is  sounding  on  its  resonant  case  the  other  be 
excited  and  brought  near  the  mouth  of  the  case,  as  in  Fig. 
162,  loud  beats  declare  the  absence  of  the  unison.  Divid- 
ing a  jar  by  a  vertical  diaphragm,  and  bringing  one  of  the 

1  In  his  admirable  experiments  on  tuninsr,  Seheibler  found  in  the 
beats  a  test  of  differences  of  temperature  of  exceeding  delicacy. 


RESULTANT  TONES.  375 

forks  over  one  of  its  halves,  and  the  other  fork  over 
the  other;  the  two  semi-cylinders  of  air  produce  beats 
by  their  interference.  But  the  diaphragm  is  not  neces- 
sary; on  removing  it,  the  beats  continue  as  before,  one 
half  of  the  same  column  of  air  interfering  with  the 
other.1 

The  intermittent  sound  of  certain  bells,  heard  more 
especially  when  their  tones  are  subsiding,  is  an  effect  of 
interference.  The  bell,  through  lack  of  symmetry,  as  ex- 
plained in  the  fourth  chapter,  vibrates  in  one  direction  a 
little  more  rapidly  than  in  the  other,  and  beats  are  the 
consequence  of  the  coalescence  of  the  two  different  rates 
of  vibration. 


RESULTANT  TONES. 

We  have  now  to  turn  from  this  question  of  interfer- 
ence to  the  consideration  of  a  new  class  of  musical  sounds, 
of  which  the  beats  were  long  considered  to  be  the  progeni- 
tors. The  sounds  here  referred  to  require  for  their  pro- 
duction the  union  of  two  distinct  musical  tones.  Where 
such  union  is  effected,  under  the  proper  conditions,  result- 
ant tones  are  generated,  which  are  quite  distinct  from 
the  primaries  concerned  in  their  production.  They  were 
discovered  in  1745,  by  a  German  organist,  named  Sorge, 
but  the  publication  of  the  fact  attracted  little  attention. 
They  were  discovered  independently  in  1754,  by  the  cele- 
brated Italian  violinist  Tartini,  and  after  him  have  been 
called  Tartini's  tones. 

To  produce  them  it  is  desirable,  if  not  necessary,  to 
have  the  two  primary  tones  of  considerable  intensity. 
Helmholtz  prefers  the  siren  to  all  other  means  of  exciting 

1  Sir  John  Herschel  and  Sir  C.  Wheatstone,  I  believe,  made  this  ex- 
periment independently. 


3T6  SOUND. 

them,  and  with  this  instrument  they  are  very  readily 
obtained.  It  requires  some  attention  at  first,  on  the  part 
of  the  listener,  to  single  out  the  resultant  tone  from  the 
general  mass  of  sound;  but,  with  a  little  practice,  this  is 
readily  accomplished;  and  though  the  unpracticed  ear 
may  fail,  in  the  first  instance,  thus  to  analyze  the  sound, 
the  clang-tint  is  influenced  in  an  unmistakable  manner  by 
the  admixture  of  resultant  tones.  I  set  Dove's  siren  in  ro- 
tation, and  open  two  series  of  holes  at  the  same  time;  with 
the  utmost  strain  of  attention,  I  am  as  yet  unable  to  hear 
the  least  symptom  of  a  resultant  tone.  Urging  the  in- 
strument to  greater  rapidity,  a  dull,  low  droning  mingles 
with  the  two  primary  sounds.  Raising  the  speed  of  rota- 
tion, the  low,  resultant  tone  rises  rapidly  in  pitch,  and 
now,  to  those  who  stand  close  to  the  instrument,  it  is  very 
audible.  The  two  series  of  holes  here  open  number  8 
and  12  respectively.  The  resultant  tone  is  in  this  case  an 
octave  below  the  deepest  of  the  two  primaries.  Opening 
two  other  series  of  orifices,  numbering  12  and  16  respec- 
tively, the  resultant  tone  is  quite  audible.  Its  rate  of 
vibration  is  one-third  of  the  rate  of  the  deepest  of  the  two 
primaries.  In  all  cases,  the  resultant  tone  is  that  which 
corresponds  to  a  rate  of  vibration  equal  to  the  difference 
of  the  rates  of  the  two  primaries. 

The  resultant  tone  here  spoken  of  is  that  actually 
heard  in  the  experiment.  But  with  finer  methods  of 
experiment  other  resultant  tones  are  proved  to  exist. 
Those  on  which  we  have  now  fixed  our  attention  are, 
however,  the  most  important.  They  are  called  difference- 
tones  by  Ilelmholtz,  in  consequence  of  the  law  just  men- 
tioned. 

To  bring  these  resultant  tones  audibly  forth,  the  pri- 
maries must,  as  already  stated,  be  forcible.  When  they 
are  feeble  the  resultants  are  unheard.  I  am  acquainted 
with  no  method  of  exciting  these  tones  more  simple  and 


EXPERIMENTAL  ILLUSTRATIONS.  377 

effectual  than  a  pair  of  suitable  singing-flames.  Two  such 
flames  may  be  caused  to  emit  powerful  notes — self-created, 
self-sustained,  and  requiring  no  muscular  effort  on  the 
part  of  the  observer  to  keep  them  going.  Here  are  two 
of  them.  The  length  of  the  shorter  of  the  two  tubes 
surrounding  these  flames  is  lOf  inches,  that  of  the  other 
is  11.4  inches.  I  hearken  to  the  sound,  and  in  the  midst 
of  the  shrillness  detect  a  very  deep  resultant  tone.  The 
reason  of  its  depth  is  manifest:  the  two  tubes  being  so 
nearly  alike  in  length,  the  difference  between  their  vi- 
brations is  small,  and  the  note  corresponding  to  this  dif- 
ference, therefore,  low  in  pitch.  Lengthening  one  of  the 
tubes  by  means  of  its  slider,  the  resultant  tone  rises 
gradually,  and  now  it  swells  surprisingly.  When  the  tube 
is  shortened  the  resultant  tone  falls,  and  thus  by  alter- 
nately raising  and  lowering  the  slider,  the  resultant  tone 
is  caused  to  rise  and  sink  in  accordance  with  the  law  which 
makes  the  number  of  its  vibrations  the  difference  between 
the  number  of  its  two  primaries. 

We  can  determine,  with  ease,  the  actual  number  of  vi- 
brations corresponding  to  any  one  of  those  resultant  tones. 
The  sound  of  the  flame  is  that  of  the  open  tube  which 
surrounds  it,  and  we  have  already  learned  (Chapter  III.) 
that  the  length  of  such  a  tube  is  half  that  of  the  sonorous 
wave  it  produces.  The  wave-length,  therefore,  correspond- 
ing to  our  1  Of -inch  tube  is  2  Of  inches.  The  velocity  of 
sound  in  air  of  the  present  temperature  is  1,120  feet  a 
second.  Bringing  these  feet  to  inches,  and  dividing  by 
2  Of ,  we  find  the  number  of  vibrations  corresponding  to  a 
length  of  lOf  inches  to  be  648  per  second. 

But  it  must  not  be  forgotten  here  that  the  air  in 
which  the  vibrations  are  actually  executed  is  much  more 
elastic  than  the  surrounding  air.  The  flame  heats  the 
air  of  the  tube,  and  the  vibrations  must,  therefore,  be 
executed  more  rapidly  than  they  would  be  in  an  ordinary 


378  SOUND. 

organ-pipe  of  the  same  length.  To  determine  the  actual 
number  of  vibrations,  we  must  fall  back  upon  our  siren; 
and  with  this  instrument  it  is  found  that  the  air  within 
the  lOf-inch  tube  executes  717  vibrations  in  a  second. 
The  difference  of  69  vibrations  a  second  is  due  to  the 
heating  of  the  aerial  column.  Carbonic  acid  and  aqueous 
vapor  are,  moreover,  the  product  of  the  flame's  combus- 
tion, and  their  presence  must  also  affect  the  rapidity  of  the 
vibration. 

Determining  in  the  same  way  the  rate  of  vibration  of 
the  11.4-inch  tube,  we  find  it  to  be  667  per  second;  the 
difference  between  this  number  and  717  is  50,  which  ex- 
presses the  rate  of  vibration  corresponding  to  the  first 
deep  resultant  tone. 

But  this  number  does  not  mark  the  limit  of  audibility. 
Permitting  the  11.4-inch  tube  to  remain  as  before, 
and  lengthening  its  neighbor,  the  resultant  tone  sinks 
near  the  limit  of  hearing.  When  the  shorter  tube  meas- 
ures 11  inches,  the  deep  sound  of  the  resultant  tone  is  still 
heard.  The  number  of  vibrations  per  second  executed 
in  this  11-inch  tube  is  700.  We  have  already  found  the 
number  executed  in  the  11. 4-inch  tube  to  be  667;  hence 
700 — 667  =  33,  which  is  the  number  of  vibrations  corre- 
sponding to  the  resultant  tone  now  plainly  heard  when  the 
attention  is  converged  upon  it.  We  here  come  very  near 
the  limit  which  Helmholtz  has  fixed  as  that  of  musical 
audibility.  Combining  the  sound  of  a  tube  17f  inches  in 
length  with  that  of  a  1  Of -inch  tube,  we  obtain  a  resultant 
tone  of  higher  pitch  than  any  previously  heard.  Now  the 
actual  number  of  vibrations  executed  in  the  longer  tube 
is  459;  and  we  have  already  found  the  vibrations  of  our 
lOf-inch  tube  to  be  717;  hence  717—459  =  258,  which 
is  the  number  corresponding  to  the  resultant  tone  now 
audible.  This  note  is  almost  exactly  that  of  one  of  our 


RESULTANT  TONES  OF  HARMONIC  INTERVALS.     379 

series  of  tuning-forks,  which  vibrates  256  times  in  a 
second. 

And  now  we  will  avail  ourselves  of  a  beautiful  check 
which  this  result  suggests  to  us.  The  well-known  fork 
which  vibrates  at  the  rate  just  mentioned  is  here,  mounted 
on  its  case,  and  I  touch  it  with  the  bow  so  lightly  that  the 
sound  alone  can  hardly  be  heard;  but  it  instantly  coa- 
lesces with  the  resultant  tone,  and  the  beats  produced  by 
their  combination  are  clearly  audible.  By  loading  the 
fork,  and  thus  altering  its  pitch,  or  by  drawing  up  the 
paper  slider,  and  thus  altering  the  pitch  of  the  flame,  the 
rate  of  these  beats  can  be  altered,  exactly  as  when  we 
compare  two  primary  tones  together.  By  slightly  varying 
the  size  of  the  flame,  the  same  effect  is  produced.  We 
cannot  fail  to  observe  how  beautifully  these  results  har- 
monize with  each  other. 

Standing  midway  between  the  siren  and  a  shrill  sing- 
ing-flame, and  gradually  raising  the  pitch  of  the  siren,  the 
resultant  tone  soon  makes  itself  heard,  sometimes  swell- 
ing out  with  extraordinary  power.  When  a  pitch-pipe  is 
blown  near  the  flame,  the  resultant  tone  is  also  heard, 
seeming,  in  this  case,  to  originate  in  the  ear  itself,  or 
rather  in  the  brain.  By  gradually  drawing  out  the  stopper 
of  the  pipe,  the  pitch  of  the  resultant  tone  is  caused  to 
vary  in  accordance  with  the  law  already  enunciated. 

The  resultant  tones  produced  by  the  combination  of 
the  ordinary  harmonic  intervals  1  are  given  in  the  follow- 
ing table: 

1  A  subject  to  be  dealt  with  in  Chapter  IX. 


380 


SOUND. 


Interval. 

Ratio  of 
vibrations. 

Difference. 

The  resultant  tone  is 
deeper  than  the  lowest 
primary  tone  by 

Octave 

1:2 

1 

0 

Fifth  . 

2:3 

1 

an  octave. 

Fourth 

3:4 

1 

a  twelfth. 

Major  third 

4:5 

1 

two  octaves. 

Minor  third 

5:6 

1 

two  octaves  and  a 

major  third. 

Major  sixth 
Minor  sixth 

3:5 

5:8 

2 
3 

a  fifth, 
major  sixth. 

The  celebrated  Thomas  Young  thought  that  these  re- 
sultant tones  were  due  to  the  coalescence  of  rapid  beats, 
which  linked  themselves  together  like  the  periodic  im- 
pulses of  an  ordinary  musical  note.  This  explanation 
harmonized  with  the  fact  that  the  number  of  the  beats, 
like  that  of  the  vibrations  of  the  resultant  tone,  is  equal 
to  the  difference  between  the  two  sets  of  vibrations.  This 
explanation,  however,  is  insufficient.  The  beats  tell  more 
forcibly  upon  the  ear  than  any  continuous  sound.  They 
can  be  plainly  heard  when  each  of  the  two  sounds  that 
produce  them  has  ceased  to  be  audible.  This  depends  in 
part  upon  the  sense  of  hearing,  but  it  also  depends  upon 
the  fact  that  when  two  notes  of  the  same  intensity  pro- 
duce beats,  the  amplitude  of  the  vibrating  air-particles 
is  at  times  destroyed,  and  at  times  doubled.  But  by 
doubling  the  amplitude  we  quadruple  the  intensity  of  the 
sound.  Hence,  when  two  notes  of  the  same  intensity  pro- 
duce beats,  the  sound  incessantly  varies  between  silence 
and  a  tone  of  four  times  the  intensity  of  either  of  the  in- 
terfering ones. . 

If,  therefore,  the  resultant  tones  were  due  to  the  beats 
of  their  primaries,  they  ought  to  be  heard,  even  when  the 
primaries  are  feeble.  But  they  are  not  heard  under  these 
circumstances.  When  several  sounds  traverse  the  same 
air,  each  particular  sound  passes  through  the  air  as  if  it 


THEORIES  OF  YOUNG  AND  HELMHOLTZ.          381 

alone  were  present,  each  particular  element  of  a  composite 
sound  asserting  its  own  individuality.  Xow,  this  is  in 
strictness  true  only  when  the  amplitudes  of  the  oscillating 
particles  are  infinitely  small.  Guided  by  pure  reasoning, 
the  mathematician  arrives  at  this  result.  The  law  is  also 
practically  true  when  the  disturbances  are  extremely 
small;  but  it  is  not  true  after  they  have  passed  a  certain 
limit.  Vibrations  which  produce  a  large  amount  of  dis- 
turbance give  birth  to  secondary  waves,  which  appeal  to 
the  ear  as  resultant  tones.  This  has  been  proved  by  Helm- 
holtz,  and,  having  proved  this,  he  inferred  further  that 
there  are  also  resultant  tones  formed  by  the  sum  of  the 
primaries,  as  well  as  by  their  difference.  He  thus  discov- 
ered the  summation-tones  before  he  had  heard  them;  and 
bringing  his  result  to  the  test  of  experiment,  he  found 
that  these  tones  had  a  real  physical  existence.  They  are 
not  at  all  to  be  explained  by  Young's  theory. 

Another  consequence  of  this  departure  from  the  law  of 
superposition  is,  that  a  single  sounding  body,  which  dis- 
turbs the  air  beyond  the  limits  of  the  law  of  superposition, 
also  produces  secondary  waves,  which  correspond  to  the 
harmonic  tones  of  the  vibrating  body.  For  example,  the 
rate  of  vibration  of  the  first  overtone  of  a  tuning-fork, 
as  stated  in  the  fourth  chapter,  is  6^  times  the  rate  of  the 
fundamental  tone.  But  Helmholtz  shows  that  a  tuning- 
fork,  not  excited  by  a  bow,  but  vigorously  struck  against  a 
pad,  emits  the  octave  of  its  fundamental  note,  this  octave 
being  due  to  the  secondary  waves  set  up  when  the  limits  of 
the  law  of  superposition  have  been  exceeded. 

These  considerations  make  it  probably  evident  to  you 
that  a  coalescence  of  musical  sounds  is  a  far  more  com- 
plicated dynamical  condition  than  you  have  hitherto  sup- 
posed it  to  be.  In  the  music  of  an  orchestra,  not  only 
have  we  the  fundamental  tones  of  every  pipe  and  of  every 
string,  but  we  have  the  overtones  of  each,  sometimes 


382  SOUND. 

audible  as  far  as  the  sixteenth  in  the  series.  We  have 
also  resultant  tones;  both  difference-tones  and  summation- 
tones;  all  trembling  through  the  same  air,  all  knocking 
at  the  self-same  tympanic  membrane.  We  have  funda- 
mental tone  interfering  with  fundamental  tone;  overtone 
with  overtone;  resultant  tone  with  resultant  tone.  And, 
besides  this,  we  have  the  members  of  each  class  interfering 
with  the  members  of  every  other  class.  The  imagination 
retires  baffled  from  any  attempt  to  realize  the  physical 
condition  of  the  atmosphere  through  which  these  sounds 
are  passing.  And,  as  we  shall  immediately  learn,  the 
aim  of  music,  through  the  centuries  during  which  it  has 
ministered  to  the  pleasure  of  man,  has  been  to  arrange 
matters  empirically,  so  that  the  ear  shall  not  suffer  from 
the  discordance  produced  by  this  multitudinous  interfer- 
ence. The  musicians  engaged  in  this  work  knew  nothing 
of  the  physical  facts  and  principles  involved  in  their  ef- 
forts; they  knew  no  more  about  it  than  the  inventors  of 
gunpowder  knew  about  the  law  of  atomic  proportions. 
They  tried  and  tried  till  they  obtained  a  satisfactory  re- 
sult; and  now,  when  the  scientific  mind  is  brought  to  bear 
upon  the  subject,  order  is  seen  rising  through  the  confu- 
sion, and  the  results  of  pure  empiricism  are  found  to  be  in 
harmony  with  natural  law. 


SUMMARY.  383 


SUMMARY  OF  CHAPTER  VIII. 

WHEN  several  systems  of  waves  proceeding  from  dis- 
tinct centres  of  disturbance  pass  through  water  or  air,  the 
motion  of  every  particle  is  the  algebraic  sum  of  the  several 
motions  impressed  upon  it. 

In  the  case  of  water,  when  the  crests  of  one  system  of 
waves  coincide  with  the  crests  of  another  system,  higher 
waves  will  be  the  result  of  the  coalescence  of  the  two  sys- 
tems. But  when  the  crests  of  one  system  coincide  with 
the  sinuses,  or  furrows,  of  the  other  system,  the  two  sys- 
tems, in  whole  or  in  part,  destroy  each  other. 

This  coalescence  and  destruction  of  two  systems  of 
waves  is  called  interference. 

Similar  remarks  apply  to  sonorous  waves.  If  in  two 
systems  of  sonorous  waves  condensation  coincides  with 
condensation,  and  rarefaction  with  rarefaction,  the  sound 
produced  by  such  coincidence  is  louder  than  that  produced 
by  either  system  taken  singly.  But  if  the  condensations 
of  the  one  system  coincide  with  the  rarefactions  of  the 
other,  a  destruction,  total  or  partial,  of  both  systems  is  the 
consequence. 

Thus,  when  two  organ-pipes  of  the  same  pitch  are 
placed  near  each  other  on  the  same  wind-chest  and  thrown 
into  vibration,  they  so  influence  each  other,  that  as  the  air 
enters  the  embouchure  of  the  one  it  quits  that  of  the  other. 
At  the  moment,  therefore,  the  one  pipe  produces  a  con- 
densation the  other  produces  a  rarefaction.  The  sounds 
of  two  such  pipes  mutually  destroy  each  other. 

When  two  musical  sounds  of  nearly  the  same  pitch 
are  sounded  together  the  flow  of  the  sound  is  disturbed  by 
beats. 

These  beats  are  due  to  the  alternate  coincidence  and 
25 


384  SOUND. 

interference  of  the  two  systems  of  sonorous  waves.  If  the 
two  sounds  be  of  the  same  intensity,  their  coincidence  pro- 
duces a  sound  of  four  times  the  intensity  of  either;  while 
their  opposition  produces  absolute  silence. 

The  effect,  then,  of  two  such  sounds,  in  combination, 
is  a  series  of  shocks,  which  we  have  called  "  beats,"  sepa- 
rated from  each  other  by  a  series  of  "  pauses." 

The  rate  at  which  the  beats  succeed  each  other  is  equal 
to  the  difference  between  the  two  rates  of  vibration. 

When  a  bell  or  disk  sounds,  the  vibrations  on  opposite 
sides  of  the  same  nodal  line  partially  neutralize  each 
other;  when  a  tuning-fork  sounds,  the  vibrations  of  its 
two  prongs  in  'part  neutralize  each  other.  By  cutting  off 
a  portion  of  the  vibrations  in  these  cases  the  sound  may 
be  intensified. 

When  a  luminous  beam,  reflected  on  to  a  screen  from 
two  tuning-forks  producing  beats,  is  acted  upon  by  the  vi- 
brations of  both,  the  intermittence  of  the  sound  is  an- 
nounced by  the  alternate  lengthening  and  shortening  of 
the  band  of  light  upon  the  screen. 

The  law  of  superposition  of  vibrations  above  enun- 
ciated is  strictly  true  only  when  the  amplitudes  are  exceed- 
ingly small.  When  the  disturbance  of  the  air  by  a  sound- 
ing body  is  so  violent  that  the  law  no  longer  holds  good, 
secondary  waves  are  formed,  which  correspond  to  the  har- 
monic tones  of  the  sounding  body. 

When  two  tones  are  rendered  so  intense  as  to  exceed 
the  limits  of  the  law  of  superposition,  their  secondary 
waves  combine  to  produce  resultant  tones. 

Resultant  tones  are  of  two  kinds;  the  one  class  corre- 
sponding to  rates  of  vibration  equal  to  the  difference  of 
the  rates  of  the  two  primaries;  the  other  class  correspond- 
ing to  rates  of  vibration  equal  to  the  sum  of  the  two  pri- 
maries. The  former  are  called  difference-tones,  the  latter 
summation-tones. 


CHAPTEK  IX. 

Combination  of  Musical  Sounds. — The  smaller  the  Two  Numbers  which 
express  the  Ratio  of  their  Rates  of  Vibration,  the  more  perfect  is 
the  Harmony  of  Two  Sounds.— Notions  of  the  Pythagoreans  re- 
garding Musical  Consonance. — Euler's  Theory  of  Consonance. — 
Theory  of  Helmholtz.— Dissonance  due  to  Beats.— Interference  of 
Primary  Tones  and  of  Overtones.— Mechanism  of  Hearing. — 
Shultze's  Bristles.— The  Otoliths.— Corti's  Fibres.— Graphic  Repre- 
sentation of  Consonance  and  Dissonance.— Musical  Chords.— The 
Diatonic  Scale.— Optical  Illustration  of  Musical  Intervals. — Lissa- 
jous's  Figures. — Sympathetic  Vibrations.— Various  Modes  of  illus- 
trating the  Composition  of  Vibrations. 

§  1.  The  Fads  of  Musical  Consonance. 

THE  subject  of  this  day's  lecture  has  two  sides,  a  physi- 
cal and  an  sesthetical.  We  have  to-day  to  study  the  ques- 
tion of  musical  consonance — to  examine  musical  sounds  in 
definite  combination  with  each  other,  and  to  unfold  the 
reason  why  some  combinations  are  pleasant  and  others  un- 
pleasant to  the  ear. 

Pythagoras  made  the  first  step  toward  the  physical  ex- 
planation of  the  musical  intervals.  This  great  philosopher 
stretched  a  string,  and  then  divided  it  into  three  equal 
parts.  At  one  of  its  points  of  division  he  fixed  it  firmly, 
thus  converting  it  into  two,  one  of  which  was  twice  the 
length  of  the  other.  He  sounded  the  two  sections  of 
the  string  simultaneously,  and  found  the  note  emitted 
by  the  short  section  to  be  the  higher  octave  of  that  emitted 
by  the  long  one.  He  then  divided  his  string  into  two 
parts,  bearing  to  each  other  the  proportion  of  2  :  3,  and 
found  that  the  notes  were  separated  by  an  interval  of  a 
fifth.  Thus,  dividing  his  string  at  different  points,  Py- 
385 


286  SOUND. 

thagoras  found  the  so-called  consonant  intervals  in  music 
to  correspond  with  certain  lengths  of  his  string;  and  he 
made  the  extremely  important  discovery  that  the  simpler 
the  ratio  of  the  two  parts  into  which  the  string  was  di- 
vided, the  more  perfect  was  the  harmony  of  the  two 
sounds.  Pythagoras  went  no  further  than  this,  and  it 
remained  for  the  investigators  of  a  subsequent  age  to 
show  that  the  strings  act  in  this  way  in  virtue  of  the 
relation  of  their  lengths  to  the  number  of  their  vibra- 
tions. Why  simplicity  should  give  pleasure  remained 
long  an  enigma,  the  only  pretence  of  a  solution  being 
that  of  Euler,  which,  briefly  expresed,  is,  that  the  human 
soul  takes  a  constitutional  delight  in  simple  calculations. 

The  double  siren  (Fig.  163)  enables  us  to  obtain  a 
great  variety  of  combinations  of  musical  sounds.  And  this 
instrument  possesses  over  all  others  the  advantage  that,  by 
simply  counting  the  number  of  orifices  corresponding  re- 
spectively to  any  two  notes,  we  obtain  immediately  the 
ratio  of  their  rates  of  vibration.  Before  proceeding  to 
these  combinations  I  will  enter  a  little  more  fully  into  the 
action  of  the  double  siren  than  has  been  hitherto  deemed 
necessary  or  desirable. 

The  instrument,  as  already  stated,  consists  of  two  of 
Dove's  sirens,  c'  and  c,  connected  by  a  common  axis,  the 
upper  one  being  turned  upside  down.  Each  siren  is 
provided  with  four  series-  of  apertures,  numbering  as 
follows: 

Upper  siren.  Lower  siren. 

Number  of  apertures.  Number  of  apertures. 
1st  Series        ....    16  18 

2d  Series         .        .        .        .15  12 

3d  Series         ....     12  10 

4th  Series       .....      9  8 

The  number  12,  it  will  be  observed,  is  common  to  both 
sirens.  I  open  the  two  series  of  12  orifices  each,  and 
urge  air  through  the  instrument;  both  sounds  flow  to- 


THE  DOUBLE  SIREN. 

FIG.  163. 


387 


388  SOUND. 

g'ether  in  perfect  unison;  the  unison  being  maintained, 
however  the  pitch  may  be  exalted.  We  have,  however, 
already  learned  (Chapter  II.)  that  by  turning  the  handle 
of  the  upper  siren  the  orifices  in  its  wind-chest  c'  are 
caused  either  to  meet  those  of  its  rotating  disk,  or  to  re- 
treat from  them,  the  pitch  of  the  upper  siren  being 
thereby  raised  or  lowered.  This  change  of  pitch  instantly 
announces  itself  by  beats.  The  more  rapidly  the  handle 
is  turned,  the  more  is  the  tone  of  the  upper  siren  raised 
above  or  depressed  below  that  of  the  lower  one,  and,  as  a 
consequence,  the  more  rapid  are  the  beats. 

Now  the  rotation  of  the  handle  is  so  related  to  the 
rotation  of  the  wind-chest  c'  that  when  the  handle  turns 
through  half  a  right  angle  the  wind-chest  turns  through 
^th  of  a  right  angle,  or  through  the  ^Vth  of  its  whole  cir- 
cumference. But  in  the  case  now  before  us,  where  the 
circle  is  perforated  by  12  orifices,  the  rotation  through 
^-th  of  its  circumference  causes  the  apertures  of  the 
upper  wind-chest  to  be  closed  at  the  precise  moments 
when  those  of  the  lower  end  are  opened,  and  vice  versa. 
It  is  plain,  therefore,  that  the  intervals  between  the  puffs 
of  the  lower  siren,  which  correspond  to  the  rarefactions  of 
its  sonorous  waves,  are  here  filled  by  the  puffs,  or  con- 
densations, of  the  upper  siren.  In  fact,  the  condensations 
of  the  one  coincide  with  the  rarefactions  of  the  other,  and 
the  absolute  extinction  of  the  sounds  of  both  sirens  is  the 
consequence. 

I  may  seem  to  you  to  have  exceeded  the  truth  here ;  for 
when  the  handle  is  placed  in  the  position  which  corre- 
sponds to  absolute  extinction,  you  still  hear  a  distinct 
sound.  And,  when  the  handle  is  turned  continuously, 
though  alternate  swellings  and  sinkings  of  the  tone  occur, 
the  sinkings  by  no  means  amount  to  absolute  silence.  The 
reason  is  this:  The  sound  of  the  siren  is  a  highly  composite 
one.  By  the  suddenness  and  violence  of  its  shocks,  not 


INTERFERENCE  AND  BEATS  OF  THE  DOUBLE  SIREN.  389 

only  does  it  produce  waves  corresponding  to  the  number  of 
its  orifices,  but  the  aerial  disturbance  breaks  up  into  sec- 
ondary waves,  which  associate  themselves  with  the  primary 
waves  of  the  instrument,  exactly  as  the  harmonics  of  a 
string,  or  of  an  open  organ-pipe,  mix  with  their  fundamen- 
tal*tone.  When  the  siren  sounds,  therefore,  it  emits,  be- 
sides the  fundamental  tone,  its  octave,  its  twelfth,  its  dou- 
ble octave,  and  so  on.  That  is  to  say,  it  breaks  the  air  up 
into  vibrations  which  have  twice,  three  times,  four  times, 
etc.,  the  rapidity  of  the  fundamental  one.  Now,  by  turn- 
ing the  upper  siren  through  V*th  of  its  circumference,  we 
extinguish  utterly  the  fundamental  tone.  But  we  do  not 
extinguish  its  octave.1  Hence,  when  the  handle  is  in  the 
position  which  corresponds  to  the  extinction  of  the  funda- 
mental tone,  instead  of  silence,  we  have  the  full  first  har- 
monic of  the  instrument.  v 

Helmholtz  has  surrounded  both  his  upper  and  his 
lower  siren  with  circular  brass  boxes,  B,  B',  each  composed 
of  two  halves,  which  can  be  readily  separated  (one  half  of 
each  box  is  removed  in  the  figure).  These  boxes  exalt 
by  their  resonance  the  fundamental  tone  of  the  instru- 
ment, and  enable  us  to  follow  its  variations  much  more 
easily  than  if  it  were  not  thus  reenforced.  It  requires  a 
certain  rapidity  of  rotation  to  reach  the  maximum  reso- 
nance of  the  brass  boxes;  but  when  this  speed  is  attained, 
the  fundamental  tone  swells  out  with  greatly  augmented 
force,  and,  if  the  handle  be  then  turned,  the  beats  succeed 
each  other  with  extraordinary  power. 

Still,  as  already  stated,  the  pauses  between  the  beats 
of  the  fundamental  tone  are  not  intervals  of  absolute 
silence,  but  are  filled  by  the  higher  octave;  and  this 
renders  caution  necessary  when  the  instrument  is  em- 
ployed to  determine  rates  of  vibration.  It  is  not  without 

1  Nor  indeed  any  of  those  tones  whose  rates  of  vibration  are  even 
multiples  of  the  rate  of  the  fundamental. 


390  SOUND. 

reason  that  I  say  so.  Wishing  to  determine  the  rate  of 
vibration  of  a  small  singing-flame,  I  once  placed  a  siren 
at  some  distance  from  it,  sounded  the  instrument,  and 
after  a  little  time  observed  the  flame  dancing  in  syn- 
chronism with  audible  beats.  I  took  it  for  granted  that 
unison  was  nearly  attained,  and,  under  this  assumption, 
determined  the  rate  of  vibration.  The  number  obtained 
was  surprisingly  low — indeed  not  more  than  half  what 
it  ought  to  be.  What  was  the  reason?  Simply  this: 
I  was  dealing,  not  with  the  fundamental  tone  of  the 
siren,  but  with  its  higher  octave.  This  octave  and  the 
flame  produced  beats  by  their  coalescence;  and  hence  the 
counter  of  the  instrument,  which  recorded  the  rate,  not  of 
the  octave,  but  of  the  fundamental,  gave  a  number  which 
was  only  half  the  true  one.  The  fundamental  tone  was 
afterward  raised  to  unison  with  the  flame.  On  approach- 
ing unison  beats  were  again  heard,  and  the  jumping  of 
the  flame  proceeded  with  an  energy  greater  than  that 
observed  in  the  case  of  the  octave.  The  counter  of  the  in- 
strument then  recorded  the  accurate  rate  of  the  flame's 
vibration. 

The  tones  first  heard  in  the  case  of  the  siren  are  al- 
ways overtones.  These  attain  sonorous  continuity  sooner 
than  the  fundamental,  flowing  as  smooth  musical  sounds 
while  the  fundamental  tone  is  still  in  a  state  of  intermit- 
tence.  The  siren  is,  however,  so  delicately  constructed 
that  a  rate  of  rotation  which  raises  the  fundamental  tone 
above  its  fellows  is  almost  immediately  attained.  And 
if  we  seek,  by  making  the  blast  feeble,  to  keep  the  speed 
of  rotation  low,  it  is  at  the  expense  of  intensity.  Hence 
the  desirability,  if  we  wish  to  examine  the  overtones,  of 
devising  some  means  by  which  a  strong  blast  and  slow 
rotation  shall  be  possible. 

Helmholtz  caused  a  spring  to  press  as  a  light  brake 
against  the  disk  of  the  siren.  Thus  raising  by  slow  de- 


BEATS  OF  OVERTONES  OF  SIREN.  391 

grees  the  speed  of  rotation,  he  was  able  deliberately  to 
notice  the  predominance  of  the  overtones  at  the  commence- 
ment, and  the  final  triumph  of  the  fundamental  tone.  He 
did  not  trust  to  the  direct  observation  of  pitch,  but  deter- 
mined the  tone  by  the  number  of  beats  corresponding  to 
one  revolution  of  the  handle  of  the  uper  siren.  Suppos- 
ing 12  orifices  to  be  opened  above  and  12  below,  the  mo- 
tion of  the  handle  through  45°  produces  interference,  and 
extinguishes  the  fundamental  tone.  The  coincidences  of 
that  tone  occur  at  the  end  of  every  rotation  of  90°. 
Hence,  for  the  fundamental  tone,  there  must  be  four  beats 
for  every  complete  rotation  of  the  handle.  Now,  Helm- 
holtz,  when  he  made  the  arrangement  just  described,  found 
that  the  first  beats  numbered,  not  4,  but  12,  for  every  revo- 
lution. They  were,  in  fact,  the  beats,  not  of  the  funda- 
mental tone,  not  even  of  the  first  overtone,  but  of  the 
second  overtone,  whose  rate  of  vibration  is  three  times 
that  of  the  fundamental.  These  beats  continued  as  long 
as  the  number  of  air-shocks  did  not  exceed  30  or  40  per 
second.  When  the  shocks  were  between  40  and  80  per 
second,  the  beats  fell  from  12  to  8  for  every  revolution  of 
the  handle.  Within  this  interval  the  first  overtone,  or 
the  octave  of  the  fundamental  tone,  was  the  most  power- 
ful, and  made  the  beats  its  own.  Not  until  the  impulses 
exceeded  80  per  second  did  the  beats  sink  to  4  per  revo- 
lution. In  other  words,  not  until  the  speed  of  rotation 
had  passed  this  limit  was  the  fundamental  tone  able  to 
assert  its  superiority  over  its  companions. 

This  premised,  we  will  combine  the  tones  in  defi- 
nite order,  while  the  cultivated  ears  here  present  shall 
judge  of  their  musical  relationship.  The  flow  of  perfect 
unison  when  the  two  series  of  12  orifices  each  are  opened 
has  been  already  heard.  I  now  open  a  series  of  8  holes 
in  the  upper,  and  of  16  in  the  lower  siren.  The  interval 
you  judge  at  once  to  be  an  octave.  If  a  series  of  9  holes 


392  SOUND. 

in  the  upper  and  of  18  holes  in  the  lower  siren  be  opened, 
the  interval  is  still  an  octave.  This  proves  that  the  inter- 
val is  not  disturbed  by  altering  the  absolute  rates  of  vi- 
bration, so  long  as  the  ratio  of  the  two  rates  remains  the 
same.  The  same  truth  is  more  strikingly  illustrated  by 
commencing  with  a  low  speed  of  rotation,  and  urging  the 
siren  to  its  highest  pitch;  as  long  as  the  orifices  are  in  the 
ratio  of  1  :  2,  we  retain  the  constant  interval  of  an  octave. 
Opening  a  series  of  10  holes  in  the  upper,  and  of  15  in  the 
lower  siren,  the  ratio  is  as  2  :  3,  and  every  musician  pres- 
ent knows  that  this  is  the  interval  of  a  fifth.  Opening  12 
holes  in  the  upper,  and  18  in  the  lower  siren,  does  not 
change  the  interval.  Opening  two  series  of  9  and  12,  or 
of  12  and  16,  we  obtain  an  interval  of  a  fourth;  the  ratio 
in  both  these  cases  being  as  3  :  4.  In  like  manner  two 
series  of  8  and  10,  or  of  12  and  15,  give  us  the  interval  of  a 
major  third;  the  ratio  in  this  case  being  as  4  :  5.  Finally, 
two  series  of  10  and  12,  or  of  15  and  18,  yield  the  inter- 
val of  a  minor  third,  which  corresponds  to  the  ratio  5:0. 
These  experiments  amply  illustrate  two  things:  First- 
ly, that  a  musical  interval  is  determined,  not  by  the  ab- 
solute number  of  vibrations  of  the  two  combining  notes, 
but  by  the  ratio  of  their  vibrations.  Secondly,  and  this 
is  of  the  utmost  significance,  that  the  smaller  the  two 
numbers  which  express  the  ratio  of  the  two  rates  of 
vibration,  the  more  perfect  is  the  consonance  of  the 
two  sounds.  The  most  perfect  consonance  is  the  unison 
1:1;  next  comes  the  octave  1:2;  after  that  the  fifth 
2:3;  then  the  fourth  3:4;  then  the  major  third  4:5; 
and  finally  the  minor  third  5  :  6.  We  can  also  open 
two  series  numbering,  respectively,  8  and  9  orifices:  this 
interval  corresponds  to  a  tone  in  music.  It  is  a  disso- 
nant combination.  Two  series  which  number  respectively 
15  and  16  orifices  make  the  interval  of  a  semi-tone:  it  is 
a  very  sharp  and  grating  dissonance. 


EULER'S  THEORY  OF  CONSONANCE.      303 


§  2.  The  Theory  of  Musical  Consonance.     Pythagoras 
and  Euler. 

Whence,  then,  does  this  arise?  Why  should  the 
smaller  ratio  express  the  more  perfect  consonance?  The 
ancients  attempted  to  solve  this  question.  The  Pythago- 
reans found  intellectual  repose  in  the  answer  "  All  is  num- 
ber and  harmony."  The  numerical  relations  of  the  seven 
notes  of  the  musical  scale  were  also  thought  by  them  to 
express  the  distances  of  the  planets  from  their  central  fire; 
hence  the  choral  dance  of  the  worlds,  the  "  music  of  the 
spheres,"  which,  according  to  his  followers,  Pythagoras 
alone  was  privileged  to  hear.  And  might  we  not  in  pass- 
ing contrast  this  glorious  superstition  with  the  groveling 
delusion  which  has  taken  hold  of  the  fantasy  of  our  day? 
Were  the  character  which  superstition  assumes  in  different 
ages  an  indication  of  man's  advance  or  retrogression,  as- 
suredly the  nineteenth  century  would  have  no  reason  to 
plume  itself,  in  comparison  with  the  sixth,  B.  c.  A  more 
earnest  attempt  to  account  for  the  more  perfect  conso- 
nance of  the  smaller  ratios  was  made  by  the  celebrated 
mathematician,  Euler,  and  his  explanation,  if  such  it 
could  be  called,  long  silenced,  if  it  did  not  satisfy,  in- 
quirers. Euler  analyzes  the  cause  of  pleasure.  We  take 
delight  in  order;  it  is  pleasant  to  us  to  observe  means 
"  cooperant  to  an  end."  But  then,  the  effort  to  discern 
order  must  not  be  so  great  as  to  weary  us.  If  the  rela- 
tions to  be  disentangled  are  too  complicated,  though  we 
may  see  the  order,  we  cannot  enjoy  it.  The  simpler  the 
terms  in  which  the  order  expresses  itself,  the  greater  is 
our  delight.  Hence  the  superiority  of  the  simpler  ratios 
in  music  over  the  more  complex  ones.  Consonance,  then, 
according  to  Euler,  was  the  satisfaction  derived  from  the 
perception  of  order  without  weariness  of  mind. 

But  in  this  theory  it  was  overlooked  that  Pythagoras 


394:  SOUND. 

himself,  who  first  experimented  on  the  musical  intervals, 
knew  nothing  about  rates  of  vibration.  It  was  forgotten 
that  the  vast  majority  of  those  who  take  delight  in  music, 
and  who  have  the  sharpest  ears  for  the  detection  of  a  dis- 
sonance, are  in  the  condition  of  Pythagoras,  knowing 
nothing  whatever  about  rates  of  ratios.  And  it  may  also 
be  added  that  the  scientific  man,  who  is  fully  informed 
upon  these  points,  has  his  pleasure  in  no  way  enhanced 
by  his  knowledge.  Euler's  explanation,  therefore,  does 
not  satisfy  the  mind,  and  it  was  reserved  for  an  eminent 
German  investigator  of  our  own  day,  after  a  profound 
analysis  of  the  entire  question,  to  assign  the  physical 
cause  of  consonance  and  dissonance — a  cause  which,  when 
once  clearly  stated,  is  so  simple  and  satisfactory  as  to 
excite  surprise  that  it  remained  so  long  without  a  dis- 
coverer. 

Various  expressions  employed  in  our  previous  lectures 
have  already,  in  part,  forestalled  Helmholtz's  explanation 
of  consonance  and  dissonance.  Let  me  here  repeat  an 
experiment  which  will,  almost  of  itself,  force  this  ex- 
planation upon  your  attention.  Before  you  are  two  jets 
of  burning  gas,  which  can  be  converted  into  singing- 
flames  by  inclosing  them  within  two  tubes  (represented 
in  Fig.  118).  The  tubes  are  of  the  same  length,  and  the 
flames  are  now  singing  in  unison.  By  means  of  a  tele- 
scopic slider  I  lengthen  slightly  one  of  the  tubes;  you 
hear  deliberate  beats,  which  succeed  each  other  so  slowly 
that  they  can  readily  be  counted.  I  augment  still  further 
the  length  of  the  tube.  The  beats  are  now  more  rapid 
than  before:  they  can  barely  be  counted.  It  is  perfectly 
manifest  that  the  shocks  of  which  you  are  now  sensible 
differ  only  in  point  of  rapidity  from  the  slow  beats  which 
you  heard  a  moment  ago.  There  is  no  breach  of  con- 
tinuity here.  We  begin  slowly,  we  gradually  increase  the 
rapidity,  until  finally  the  succession  of  the  beats  is  so 


BEATS  A  POSSIBLE  CAUSE  OF  DISSONANCE.      395 

rapid  as  to  produce  that  particular  grating  effect  which 
every  musician  that  hears  it  would  call  dissonance.  Let 
us  now  reverse  the  process,  and  pass  from  these  quick 
beats  to  slow  ones.  The  same  continuity  of  the  phe- 
nomenon is  noticed.  By  degrees  the  beats  separate  from 
each  other  more  and  more,  until  finally  they  are  slow 
enough  to  be  counted.  Thus  these  singing-flames  enable 
us  to  follow  the  beats  with  certainty,  until  they  cease  to 
be  beats,  and  are  converted  into  dissonance. 

This  experiment  proves  conclusively  that  dissonance 
may  be  produced  by  a  rapid  succession  of  beats;  and  I 
imagine  this  cause  of  dissonance  would  have  been  pointed 
out  earlier,  had  not  men's  minds  been  thrown  off  the  prop- 
er track  by  the  theory  of  "  resultant  tones  "  enunciated  by 
Thomas  Young.  Young  imagined  that,  when  they  were 
quick  enough,  the  beats  ran  together  to  form  a  resultant 
tone.  He  imagined  the  linking  together  of  the  beats  to 
be  precisely  analogous  to  the  linking  together  of  simple 
musical  impulses;  and  he  was  strengthened  in  this  notion 
by  the  fact  already  adverted  to,  that  the  first  difference- 
tone,  that  is  to  say,  the  loudest  resultant  tone,  corresponded, 
as  the  beats  do,  to  a  rate  of  vibration  equal  to  the  differ- 
ence of  the  rates  of  the  two  primaries.  The  fact,  how- 
ever, is,  that  the  effect  of  beats  upon  the  ear  is  altogether 
different  from  that  of  the  successive  impulses  of  an  ordi- 
nary musical  tone. 

§  3.  Sympathetic  Vibrations. 

But  to  grasp,  in  all  its  fullness,  the  new  theory  of  mu- 
sical consonance  some  preliminary  studies  will  be  neces- 
sary. And  here  I  would  ask  you  to  call  to  mind  the  ex- 
periments (in  Chapter  III.)  by  which  the  division  of  a 
string  into  its  harmonic  segments  was  illustrated.  This 
was  done  by  means  of  little  paper  riders,  which  were  un- 


396  SOUND. 

horsed,  or  not,  according  as  they  occupied  a  ventral  seg- 
ment or  a  node  upon  the  string.  Before  you  at  present 
is  the  sonometer,  employed  in  the  experiments  just  re- 
ferred to.  Along  it,  instead  of  one,  are  stretched  two 
strings,  about  three  inches  asunder.  By  means  of  a  key 
these  strings  are  brought  into  unison.  And  now  I  place 
a  little  paper  rider  upon  the  middle  of  one  of  them,  and 
agitate  the  other.  What  occurs?  The  vibrations  of  the 
sounding  string  are  communicated  to  the  bridges  on 
which  it  rests,  and  through  the  bridges  to  the  other 
string.  The  individual  impulses  are  very  feeble,  but, 
because  the  two  strings  are  in  unison,  the  impulses  can 
so  accumulate  as  finally  to  toss  the  rider  off  the  untouched 
string. 

Every  experiment  executed  with  the  riders  and  a  sin- 
gle string  may  be  repeated  with  these  two  unisonant 
strings.  Damping,  for  instance,  one  of  the  strings,  at  a 
point  one-fourth  of  its  length  from  one  of  its  ends,  and 
placing  the  red  and  blue  riders  formerly  employed,  not  on 
the  nodes  and  ventral  segments  of  the  damped  string, 
but  at  points  upon  the  second  string  exactly  opposite  to 
those  nodes  and  segments,  when  the  bow  is  passed  across 
the  shorter  segment  of  the  damped  string,  the  five  red 
riders  on  the  adjacent  string  are  unhorsed,  while  the  four 
blue  ones  remain  tranquilly  in  their  places.  By  relaxing 
one  of  the  strings,  it  is  thrown  out  of  unison  with  the 
other,  and  then  all  efforts  to  unhorse  the  riders  are  un- 
availing. That  accumulation  of  impulses,  which  unison 
alone  renders  possible,  cannot  here  take  place,  and  the 
consequence  is,  that  however  great  the  agitation  of  the 
one  string  may  be,  it  fails  to  produce  any  sensible  effect 
upon  the  other. 

The  influence  of  synchronism  may  be  illustrated  in  a 
still  more  striking  manner,  by  means  of  two  tuning-forks 
which  sound  the  same  note.  Two  such  forks  mounted  on 


SYMPATHETIC  VIBRATIONS.  397 

their  resonant  supports  are  placed  upon  the  table.  I  draw 
the  bow  vigorously  across  one  of  them,  permitting  the 
other  fork  to  remain  untouched.  On  stopping  the  agi- 
tated fork,  the  sound  is  enfeebled,  but  by  no  means 
quenched.  Through  the  air  and  through  the  wood  the 
vibrations  have  been  conveyed  from  fork  to  fork,  and  the 
untouched  fork  is  the  one  you  now  hear.  When,  by 
means  of  a  morsel  of  wax,  a  small  coin  is  attached  to  one  of 
the  forks,  its  power  of  influencing  the  other  ceases;  the 
change  in  the  rate  of  vibration,  if  not  very  small,  so  de- 
stroys the  sympathy  between  the  two  forks  as  to  render  a 
response  impossible.  On  removing  the  coin  the  untouched 
fork  responds  as  before. 

This  communication  of  vibrations  through  wood  and 
air  may  be  obtained  when  the  forks,  mounted  on  their 
cases,  stand  several  feet  apart.  But  the  vibrations  may 
also  be  communicated  through  the  air  alone.  Holding 
the  resonant  case  of  a  vigorously  vibrating  fork  in  my 
hand,  I  bring  one  of  its  prongs  near  an  unvibrating  one, 
placing  the  prongs  back  to  back,  but  allowing  a  space  of 
air  to  exist  between  them.  Light  as  is  the  vehicle,  the  ac- 
cumulation of  impulses,  secured  by  the  perfect  unison  of 
the  two  forks,  enables  the  one  to  set  the  other  in  vibra- 
tion. Extinguishing  the  sound  of  the  agitated  fork,  that 
which  a  moment  ago  was  silent  continues  sounding, 
having  taken  up  the  vibrations  of  its  neighbor.  Ee- 
moving  one  of  the  forks  from  its  resonant  case,  and 
striking  it  against  a  pad,  it  is  thrown  into  strong  vibra- 
tion. Held  free  in  the  air,  its  sound  is  audible.  But, 
on  bringing  it  close  to  the  silent  mounted  fork,  out  of 
the  silence  rises  a  full  mellow  sound,  which  is  due,  not 
to  the  fork  originally  agitated,  but  to  its  sympathetic 
neighbor. 

Various  other  examples  of  the  influence  of  synchro- 
nism, already  brought  forward,  will  occur  to  you  here; 


398  SOUND. 

and  cases  of  the  kind  might  be  indefinitely  multiplied. 
If  two  clocks,  for  example,  with  pendulums  of  the  same 
period  of  vibration,  be  placed  against  the  same  wall,  and 
if  one  of  the  clocks  is  set  going  and  the  other  not,  the 
ticks  of  the  moving  clock,  transmitted  through  the  wall, 
will  act  upon  its  neighbor.  The  quiescent  pendulum, 
moved  by  a  single  tick,  swings  through  an  extremely  mi- 
nute arc;  but  it  returns  to  the  limit  of  its  swing  just  in 
time  to  receive  another  impulse.  By  the  continuance  of 
this  process,  the  impulses  so  add  themselves  together  as 
finally  to  set  the  clock  a-going.  It  is  by  this  timing  of 
impulses  that  a  properly-pitched  voice  can  cause  a  glass 
to  ring,  and  that  the  sound  of  an  organ  can  break  a  par- 
ticular window-pane. 

§  4.  Sympathetic  Vibration  in  Relation  to  the  Human 
Ear. 

If  I  dwell  so  fully  upon  this  subject,  it  is  for  the  pur- 
pose of  rendering  intelligible  the  manner  in  which  sono- 
rous motion  is  communicated  to  the  auditory  nerve.  In 
the  organ  of  hearing,  in  man,  we  have  first  of  all  the 
external  orifice  of  the  ear,  closed  at  the  bottom  by  the 
circular  tympanic  membrane.  Behind  that  membrane  is 
the  drum  of  the  ear,  this  cavity  being  separated  from  the 
space  between  it  and  the  brain  by  a  bony  partition,  in 
which  there  are  two  orifices,  the  one  round  and  the  other 
oval.  These  orifices  are  also  closed  by  fine  membranes. 
Across  the  drum  stretches  a  series  of  four  little  bones. 
The  first,  called  the  hammer,  is  attached  to  the  tympanic 
membrane;  the  second,  called  the  anvil,  is  connected  by 
a  joint  with  the  hammer;  a  third  little  round  bone  con- 
nects the  anvil  with  the  stirrup-bone,  the  base  of  which 
is  planted  against  the  membrane  of  the  oval  orifice  just 
referred  to.  This  oval  membrane  is  almost  covered  by 


ACOUSTIC  ARRANGEMENTS   WITHIN  THE  EAR.    399 

the  stirrup-bone,  a  narrow  rim  only  of  the  membrane 
surrounding  the  bone  being  left  uncovered.  Behind  the 
bony  partition,  and  between  it  and  the  brain,  we  have  the 
extraordinary  organ  called  the  labyrinth,  filled  with  water, 
over  the  lining  membrane  of  which  are  distributed  the 
terminal  fibres  of  the  auditory  nerve.  When  the  tym- 
panic membrane  receives  a  shock,  it  is  transmitted  through 
the  series  of  bones  above  referred  to,  being  concentrated 
on  the  membrane  against  which  the  base  of  the  stirrup- 
bone  is  fixed.  The  membrane  transfers  the  shock  to  the 
water  of  the  labyrinth,  which,  in  its  turn,  transfers  it  to 
the  nerves. 

The  transmission,  however,  is  not  direct.  At  a  cer- 
tain place  within  the  labyrinth  exceedingly  fine  elastic 
bristles,  terminating  in  sharp  points,  grow  up  between 
the  terminal  nerve-fibres.  These  bristles,  discovered  by 
Max  Schultze,  are  eminently  calculated  to  sympathize 
with  such  vibrations  of  the  water  as  correspond  to  their 
proper  periods.  Thrown  thus  into  vibration,  the  bristles 
stir  the  nerve-fibres  which  lie  between  their  roots.  At 
another  place  in  the  labyrinth  we  have  little  crystalline 
particles  called  otolites — the  Hb'rsteine  of  the  Germans 
— imbedded  among  the  nervous  filaments,  which,  when 
they  vibrate,  exert  an  intermittent  pressure  upon  the  ad- 
jacent nerve-fibres.  The  otolites  probably  serve  a  dif- 
ferent purpose  from  that  of  the  bristles  of  Schultze. 
They  are  fitted,  by  their  weight,  to  accept  and  prolong 
the  vibrations  of  evanescent  sounds,  which  might  other- 
wise escape  attention,  while  the  bristles  of  Schultze,  be- 
cause of  their  extreme  lightness,  would  instantly  yield  up 
an  evanescent  motion.  They  are,  on  the  other  hand,  emi- 
nently fitted  for  the  transmission  of  continuous  vibrations. 

Finally,  there  is  in  the  labyrinth  an  organ,  discovered 
by  the  Marchese  Corti,  which  is  to  all  appearance  a  musi- 
cal instrument,  with  its  cords  so  stretched  as  to  accept 


400  SOUND. 

vibrations  of  different  periods,  and  transmit  them  to  the 
nerve-filaments  which  traverse  the  organ.  Within  the 
ears  of  men,  and  without  their  knowledge  or  contrivance, 
this  lute  of  3,000  strings  l  has  existed  for  ages,  accepting 
the  music  of  the  outer  world  and  rendering  it  fit  for  re- 
ception by  the  brain.  Each  musical  tremor  which  falls 
upon  this  organ  selects  from  the  stretched  fibres  the  one 
appropriate  to  its  own  pitch,  and  throws  it  into  unisonant 
vibration.  And  thus,  no  matter  how  complicated  the  mo- 
tion of  the  external  air  may  be,  these  microscopic  strings 
can  analyze  it  and  reveal  the  constituents  of  which  it  is 
composed.  Surely,  inability  to  feel  the  stupendous  won- 
der of  what  is  here  revealed  would  imply  incompleteness 
of  mind;  and  surely  those  who  practically  ignore,  or  fear 
them,  must  be  ignorant  of  the  ennobling  influence  which 
such  discoveries  may  be  made  to  exercise  upon  both  the 
emotions  and  the  understanding  of  man. 

§  5.  Consonant  Intervals  in  Relation  to  the  Human  Ear. 

This  view  of  the  use  of  Corti's  fibres  is  theoretical; 
but  it  comes  to  us  commended  by  every  appearance  of 
truth.  It  will  enable  us  to  tie  together  many  things, 
whose  relations  it  would  be  otherwise  difficult  to  discern. 
When  a  musical  note  is  sounded  its  corresponding  Corti's 
fibre  resounds,  being  moved,  as  a  string  is  moved  by  a 
second  unisonant  string.  And  when  two  sounds  coalesce 
to  produce  beats,  the  intermittent  motion  is  transferred 
to  the  proper  fibre  within  the  ear.  But  here  it  is  to  be 
noted  that,  for  the  same  fibre  to  be  affected  simultaneously 
by  two  different  sounds,  it  must  not  be  far  removed  in 
pitch  from  either  of  them.  Call  to  mind  our  repetition 
of  Melde's  experiments  (in  Chapter  III.).  You  then  had 
frequent  occasion  to  notice  that  even,  before  perfect  syn- 
chronism had  been  established  between  the  string  and  the 
1  According  to  Kolliker,  this  is  the  number  of  fibres  in  Corti's  organ. 


RELATION  OF  BEATS  TO  CORTI'S  ORGAN.         401 

tuning-fork  to  which  it  was  attached,  the  string  began  to 
respond  to  the  fork.  But  you  also  noticed  how  rapidly 
the  vibrating  amplitude  of  the  string  increased,  as  it  came 
close  to  perfect  synchronism  with  the  vibrating  fork.  On 
approaching  unison  the  string  would  open  out,  say  to 
an  amplitude  of  an  inch;  and  then  a  slight  tightening  or 
slackening,  as  the  case  might  be,  would  bring  it  up  to  uni- 
son, and  cause  it  to  open  out  suddenly  to  an  amplitude  of 
six  inches. 

So  also  in  reference  to  the  experiment  made  a  moment 
ago  with  the  sonometer;  you  noticed  that  the  unhorsing 
of  the  paper  riders  was  preceded  by  a  fluttering  of  the 
bits  of  paper;  showing  that  the  sympathetic  response  of 
the  second  string  had  begun,  though  feebly,  prior  to  per- 
fect synchronism.  Instead  of  two  strings,  conceive  three 
strings,  all  nearly  of  the  same  pitch,  to  be  stretched  upon 
the  sonometer;  and  suppose  the  vibrating  period  of  the 
middle  string  to  lie  midway  between  the  periods  of  its 
two  neighbors,  being  a  little  higher  than  the  one  and  a 
little  lower  than  the  other.  Each  of  the  side  strings, 
sounded  singly,  would  cause  the  middle  string  to  respond. 
Sounding  the  two  side  strings  together  they  would  pro- 
duce beats;  the  corresponding  intermittence  would  be 
propagated  to  the  central  string,  which  would  beat  in  syn- 
chronism with  the  beats  of  its  neighbors.  In  this  way 
we  make  plain  to  our  minds  how  a  Corti's  fibre  may,  to 
some  extent,  take  up  the  vibrations  of  a  note,  nearly,  but 
not  exactly,  in  unison  with  its  own;  and  that  when  two 
notes  close  to  the  pitch  of  the  fibre  act  upon  it  together,  , 
their  beats  are  responded  to  by  an  intermittent  motion 
on  the  part  of  the  fibre.  This  power  of  sympathetic 
vibration  would  fall  rapidly  on  both  sides  of  the  perfect 
unison,  so  that  on  increasing  the  interval  between  the  two 
notes,  a  time  would  soon  arrive  when  the  same  fibre  would 
refuse  to  be  acted  on  simultaneously  by  both.  Here  the 


402  SOUND. 

condition  of  the  organ,  necessary  for  the  perception  of 
audible  beats,  would  cease. 

In  the  middle  region  of  the  piano-forte,  with  the  in- 
terval of  a  semitone,  the  beats  are  sharp  and  distinct,  fall- 
ing indeed  upon  the  ear  as  a  grating  dissonance.  Extend- 
ing the  interval  to  a  whole  tone,  the  beats  become  more 
rapid,  but  less  distinct.  With  the  interval  of  a  minor 
third  between  the  two  notes,  the  beats  in  the  middle  re- 
gion of  the  scale  cease  to  be  sensible.  But  this  smoothen- 
ing  of  the  sound  is  not  wholly  due  to  the  augmented  rapid- 
ity of  the  beats.  It  is  due  in  part  to  the  fact,  for  which 
the  foregoing  considerations  have  prepared  us,  that  the 
two  notes  here  sounded  are  too  far  removed  from  that  of 
the  intermediate  Corti's  fibre  to  affect  it  powerfully.  By 
ascending  to  the  higher  regions  of  the  scale  we  can  pro- 
duce, with  a  narrower  interval  than  the  minor  third,  the 
same,  or  even  a  greater  number  of  beats,  which  are  sharply 
distinguishable  because  of  the  closeness  of  their  component 
notes.  In  the  very  highest  regions  of  the  scale,  however, 
the  beats,  when  they  become  very  rapid,  cease  to  appeal  as 
roughness  to  the  ear. 

Hence  both  the  rapidity  of  the  beats,  and  the  width  of 
the  interval,  enter  into  the  question  of  consonance.  Helm- 
holtz  judges  that  in  the  middle  and  higher  regions  of  the 
musical  scale,  when  the  beats  reach  33  per  second,  the  dis- 
sonance reaches  its  maximum.  Both  slower  and  quicker 
beats  have  a  less  grating  or  dissonant  effect.  When  the 
beats  are  very  slow,  they  may  be  of  advantage  to  the  mu- 
sic; and,  when  they  reach  132  per  second,  their  roughness 
is  no  longer  discernible. 

Thanks  to  Helmholtz,  whose  views  I  have  here  sought 
to  express  in  the  briefest  possible  language,  we  are  now  in 
a  condition  to  grapple  with  the  question  of  musical  inter- 
vals, and  to  give  the  reason  why  some  are  consonant  and 
some  dissonant  to  the  ear.  Circumstanced  as  we  are  upon 


RELATION  OF  CONSONANCE  TO  OVERTONES.     403 

earth,  all  our  feelings  and  emotions,  from  the  lowest  sensa- 
tion to  the  highest  aesthetic  consciousness,  have  a  me- 
chanical cause:  though  it  may  be  forever  denied  to  us  to 
take  the  step  from  cause  to  effect;  or  to  understand  why 
the  agitations  of  nervous  matter  can  awaken  the  delights 
which  music  imparts.  Take,  then,  the  case  of  a  violin. 
The  fundamental  tone  of  every  string  of  this  instrument 
is  demonstrably  accompanied  by  a  crowd  of  overtones;  so 
that,  when  two  violins  are  sounded,  we  have  not  only  to 
take  into  account  the  consonance,  or  dissonance,  of  the 
fundamental  tones,  but  also  those  of  the  higher  tones  of 
both.  Supposing  two  strings  sounded  whose  fundamental 
tones,  and  all  of  whose  partial  tones,  coincide,  we  have 
then  absolute  unison;  and  this  we  actually  have  when  the 
ratio  of  vibration  is  1:1.  So  also  when  the  ratio  of 
vibration  is  accurately  1:2,  each  overtone  of  the  funda- 
mental finds  itself  in  absolute  coincidence  with  either 
the  fundamental  tone  or  some  higher  tone  of  the  octave. 
There  is  no  room  for  beats  or  dissonance.  When  we  ex- 
amine the  interval  of  a  fifth,  with  a  ratio  of  2  :  3,  we  find 
the  coincidence  of  the  partial  tones  of  the  two  strings 
so  perfect  as  almost,  though  not  wholly,  to  exclude  every 
trace  of  dissonance.  Passing  on  to  the  other  intervals,  we 
find  the  coincidence  of  the  partial  tones  less  perfect,  as 
the  numbers  expressing  the  ratio  of  the  vibrations  become 
more  large.  Thus,  the  dissonance  of  intervals  whose  rates 
of  vibration  can  only  be  expressed  by  large  numbers,  is 
not  to  be  ascribed  to  any  mystic  quality  of  the  numbers 
themselves,  but  to  the  fact  that  the  fundamental  tones 
which  require  such  numbers  are  inexorably  accompanied 
by  partial  tones  whose  coalescence  produces  beats,  these 
producing  the  grating  effect  known  as  dissonance. 

§  6.  Graphic  Representation  of  Consonance  and  Dissonance. 

Helmholtz    has    attempted   to    represent    this    result 
graphically,  and  from  his  work  I  copy,  with  some  modi- 


404  SOUND. 

fication,  tlie  next  two  diagrams.  He  assumes,  as  already 
stated,  the  maximum  dissonance  to  correspond  to  33  beats 
per  second;  and  he  seeks  to  express  different  degrees  of 
dissonance  by  lines  of  different  lengths.  The  horizontal 
line  c'  c",  Fig.  164,  represents  a  range  of  the  musical  scale 
in  which  c"  is  our  middle  c,  with  528  vibrations,  and  c' 
the  lower  octave  of  c".  The  distance  from  any  point  of 
this  line  to  the  curve  above  it  represents  the  dissonance 
corresponding  to  that  point.  The  pitch  here  is  supposed 
to  ascend  continuously,  and  not  by  jumps.  Supposing, 
for  example,  two  performers  on  the  violin  to  start  with  the 
same  note  c',  and  that,  while  one  of  them  continues  to 
sound  that  note,  the  other  gradually  and  continuously 
shortens  his  string,  thus  gradually  raising  its  pitch  up  to 
the  octave  c".  The  effect  upon  the  ear  would  be  repre- 

FIG.  164. 


sented  by  the  irregular  curved  line  in  Fig.  164.  Soon 
after  the  unison,  which  is  represented  by  contact  at  c',  is 
departed  from,  the  curve  suddenly  rises,  showing  the  disso- 
nance here  to  be  the  sharpest  of  all.  At  e',  the  curve 
approaches  the  straight  line  c'  c",  and  this  point  corre- 
sponds to  the  major  third.  At  f  the  approach  is  still 
nearer,  and  this  point  corresponds  to  the  fourth.  At  g' 
the  curve  almost  touches  the  straight  line,  indicating  that 
at  this  point,  which  corresponds  to  the  fifth,  the  disso- 


CONSONANCE  AND  DISSONANCE.  405 

nance  almost  vanishes.  At  a'  we  have  the  major  sixth; 
while  at  c",  where  the  one  note  is  an  octave  above  the 
other,  the  dissonance  entirely  vanishes.  The  e  s'  and  the 
a  s',  of  this  diagram,  are  the  German  names  of  a  flat  third 
and  a  flat  sixth. 

Maintaining  the  same  fundamental  note  c',  and  passing 
through  the  octave  above  c",  the  various  degrees  of  conso- 
nance and  dissonance  are  those  shown  in  Fig.  165.  That 

FIG.  165. 


is  to  say,  beginning  with  the  octave  c' — c",  and  gradually 
elevating  the  pitch  of  one  of  the  strings,  till  it  reaches  c'", 
the  octave  of  c",  the  curved  line  represents  the  effect  upon 
the  ear.  We  see,  from  both  these  curves,  that  dissonance 
is  the  general  rule,  and  that  only  at  certain  definite  points 
does  the  dissonance  vanish,  or  become  so  decidedly  en- 
feebled as  not  to  destroy  the  harmony.  These  points  cor- 
respond to  the  places  where  the  numbers  expressing  the 
ratio  of  the  two  rates  of  vibration  are  small  whole  numbers. 
It  must  be  remembered  that  these  curves  are  constructed 
on  the  supposition  that  the  beats  are  the  cause  of  the 
dissonance;  and  the  agreement  between  calculation  and 
experience  sufficiently  demonstrates  tjie  truth  of  the 
assumption.1 

1  The  comparison  employed  by  Mr.  Sedley  Taylor  appeals  with 
graphic  truth  to  a  mountaineer.  Considering  the  above  curve  to  repre- 
sent a  mountain-chain,  he  calls  the  discords  peaks,  and  the  concords 
passes. 


406  SOUND. 

You  have  thus  accompanied  me  to  the  verge  of  the 
Physical  portion  of  the  science  of  Acoustics,  and  through 
the  aesthetic  portion  I  have  not  the  knowledge  of  music  ne- 
cessary to  lead  you.  I  will  only  add  that,  in  comparing 
three  or  more  sounds  together,  that  is  to  say,  in  choosing 
them  for  chords,  we  are  guided  by  the  principles  just  men- 
tioned. We  choose  sounds  which  are  in  harmony  with 
the  fundamental  sound  and  with  each  other.  In  choosing 
a  series  of  sounds  for  combination  two  by  two,  the  simplic- 
ity alone  of  the  ratios  would  lead  us  to  fix  on  those  ex- 
pressed by  the  numbers  1,  f,  f,  f,  f,  2;  these  being  the 
simplest  ratios  that  we  can  have  within  an  octave.  But, 
when  the  notes  represented  by  these  ratios  are  sounded  in 
succession,  it  is  found  that  the  intervals  between  1  and  £ , 
and  between  $  and  2,  are  wider  than  the  others,  and  re- 
quire the  interpolation  of  a  note  in  each  case.  The  notes 
chosen  are  such  as  form  chords,  not  with  the  fundamental 
tone,  but  with  the  note  f  regarded  as  a  fundamental  tone. 
The  ratios  of  these  two  notes  with  the  fundamental  are  f 
and  *£-.  Interpolating  these,  we  have  the  eight  notes  of 
the  natural  or  diatonic  scale,  expressed  by  the  following 
names  and  ratios: 

Names.      C.     D.      E.     F.     G.     A.     B.     C'. 

Intervals.      1st.    2d.    3d.    4th.   5th.  6th.   7th.  8th. 
Rates  of  vibration.       1,      f,       fc      f,      f,      f,      Y,      2. 

Multiplying  these  ratios  by  24,  to  avoid  fractions,  we 
obtain  the  following  series  of  whole  numbers,  which  ex- 
press the  relative  rates  of  vibration  of  the  notes  of  the 
diatonic  scale: 

24,  27,  30,  32,  36,  40,  45,  48. 

The  meaning  of  the  terms  third,  fourth,  fifth,  etc., 
which  we  have  so  often  applied  to  the  musical  intervals, 
is  now  apparent;  the  term  has  reference  to  the  position  of 
the  note  in  the  scale. 


MECHANICAL  STUDIES.  407 

§  7.  Composition  of  Vibrations. 

In  our  second  lecture  I  referred  to,  and  in  part  illus- 
trated, a  method  devised  by  M.  Lissajous  for  studying 
musical  vibrations.  By  means  of  a  beam  of  light  reflected 
from  a  mirror  attached  to  a  tuning-fork,  the  fork  was 
made  to  write  the  story  of  its  own  motion.  In  our  last 
lecture  the  same  method  was  employed  to  illustrate  opti- 
cally the  phenomenon  of  beats.  I  now  propose  to  apply 
it  to  the  study  of  the  composition  of  the  vibrations  which 
constitute  the  principal  intervals  of  the  diatonic  scale. 
We  must,  however,  prepare  ourselves  for  the  thorough 
comprehension  of  this  subject  by  a  brief  preliminary  ex- 
amination of  the  vibrations  of  a  common  pendulum. 

Such  a  pendulum  hangs  before  you.  It  consists  of  a 
wire  carefully  fastened  to  a  plate  of  iron  at  the  roof  of  the 
house,  and  bearing  a  copper  ball  weighing  10  Ibs.  I  draw 
the  pendulum  aside  and  let  it  go;  it  oscillates  to  and  fro 
almost  in  the  same  plane. 

I  say  "  almost,"  because  it  is  practically  impossible  to 
suspend  a  pendulum  without  some  little  departure  from 
perfect  symmetry  around  its  point  of  attachment.  In 
consequence  of  this,  the  weight  deviates  sooner  or  later 
from  a  straight  line,  and  describes  an  oval  more  or  less 
elongated.  Some  years  ago  this  circumstance  presented  a 
serious  difficulty  to  those  who  wished  to  repeat  M.  Fou- 
cault's  celebrated  experiment,  demonstrating  the  rotation 
of  the  earth. 

Nevertheless,  in  the  case  now  before  us,  the  pendu- 
lum is  so  carefully  suspended  that  its  deviation  from  a 
straight  line  is  not  at  first  perceptible.  Let  us  suppose 
the  amplitude  of  its  oscillation  to  be  represented  by  the 
dotted  line  a  &,  Fig.  166.  The  point  d,  midway  between 
a  and  6,  is  the  pendulum's  point  of  rest.  When  drawn 
aside  from  this  point  to  &,  and  let  go,  it  will  return  to  d, 
and  in  virtue  of  its  momentum  will  pass  on  to  a.  There 


408 


SOUND. 


FIG.  1G6. 


it  comes  momentarily  to  rest,  and  returns  through  d  to  &. 
And  thus  it  will  continue  to  oscillate 
until  its  motion  is  expended. 

The  pendulum  having  first  reached 
the  limit  of  its  swing  at  6,  let  us  sup- 
pose  a   push   in   a   direction   perpen- 
dicular to  a  1)  imparted  to  it;  that  is 
to  say,  in  the  direction  b  c.     Suppos- 
ing  the   time   required   by   the   pen- 
dulum to  swing  from  &  to  a  to  be 
one  second,1  then  the  time  required  to  swing  from  &  to 
FIG.  167.         d  will  be  half  a  second.     Suppose,  fur- 
ther, the  force  applied  at  &  to  be  such  as 
would  carry  the  bob,  if  free  to  move  in 
that  direction  alone,  to  c  in  half  a  second, 
and  that  the  distance  &  c  is  equal  to  &  tZ, 
the  question  then  occurs,  where  will  the 
bob  really  find  itself  at  the  end  of  half 
a  second?     It  is  perfectly  manifest  that 
both  forces  are  satisfied  by  the  pendulum 
reaching  the  point  e,  exactly  opposite  the 
centre   d,   in   half   a   second.     To   reach 
this  point,  it  can  be  shown  that  it  must 
describe  the  circular  arc  &  e,  and  it  will 
pursue  its  way  along  the  continuation  of 
the  same  arc,  to  a,  and  then  pass  round 
to  &.     Thus,  by  the  rectangular  impulse 
the  rectilinear  oscillation  is  converted  into 
a  rotation,  the  pendulum  describing  a  cir- 
cle, as  shown  in  Fig.  167. 

If  the  force  applied  at  &  be  sufficient 
to  urge  the  weight  in  half  a  second 
through  a  greater  distance  than  b  c,  the 

1  This  supposition  is  of  course  mn-le  for  the  sake  of  simplicity,  the 
real  period  of  oscillation  of  a  pendulum  28  feet  long  being  between  two 
and  three  seconds. 


THE  PENDULUM.  409 

pendulum  will  describe  an  ellipse,  with  the  lines  a  b  for 
its  smaller  axis;  if,  on  the  contrary,  the  force  applied  at  b 
urge  the  pendulum  in  half  a  second  through  a  distance  less 
than  b  c,  the  weight  will  describe  an  ellipse,  with  the  line 
a  b  for  its  greater  axis. 

Let  us  now  inquire  what  occurs  when  the  rectangular 
impulse  is  applied  at  the  moment  the  ball  is  passing 
through  its  position  of  rest  at  d. 

Supposing  the  pendulum  to  be  moving  from  a  to  &, 
Fig.  168,  and  that  at  d  a  shock  is  imparted  to  it  sufficient 
Fio. 


of  itself  to  carry  it  in  half  a  second  to  c;  it  is  here  mani- 
fest that  the  resultant  motion  will  be  along  the  straight 
line  d  g  lying  between  b  d  and  d  c.  The  pendulum  will 
return  along  this  line  to  d,  and  pass  on  to  h.  In  this  case, 
therefore,  the  pendulum  will  describe  a  straight  line,  g  h, 
oblique  to  its  original  direction  of  oscillation. 

Supposing  the  direction  of  motion  at  the  moment  the 
push  is  applied  to  be  from  b  to  a,  instead  of  from  a  to  &, 
it  is  manifest  that  the  resultant  here  will  also  be  a  straight 
line  oblique  to  the  primitive  direction  of  oscillation;  but 
its  obliquity  will  be  that  shown  in  Fig.  169. 

When  the  impulse  is  imparted  to  the  pendulum  neither 
at  the  centre  nor  at  the  limit  of  its  swing,  but  at  some 
point  between  both,  we  obtain  neither  a  circle  nor  a 
straight  line,  but  something  between  both.  We  have,  in 
fact,  a  more  or  less  elongated  ellipse  with  its  axis  oblique 
to  a  b}  the  original  direction  of  vibration.  If,  for  example, 


410 


SOUND. 


the  impulse  be  imparted  at  d',  Fig.  170,  while  the  pendu- 
lum is  moving  toward  &,  the  position  of  the  ellipse  will  be 
that  shown  in  Fig.  170;  but  if  the  push  at  d'  be  given 
when  the  motion  is  toward  a,  then  the  position  of  the 
ellipse  will  be  that  represented  in  Fig.  171. 

FIG.  170.  FIG.  171. 


By  the  method  of  M.  Lissajous  we  can  combine  the 
rectangular  vibrations  of  two  tuning-forks,  a  subject 
which  I  now  wish  to  illustrate  before  you.  In  front  of 


FIG.  172. 


an  electric  lamp,  L,  Fig.  172,  is  placed  a  large  tuning-fork, 
T',  fixed  in  a  stand  horizontally,   and  provided  with  a 


COMPOSITION  OF  SONOROUS  VIBRATIONS.         41 1 

mirror,  on  which  a  narrow  beam  of  light,  L  T',  is  per- 
mitted to  fall.  The  beam  is  thrown  back,  by  reflection. 
In  the  path  of  the  reflected  beam  is  placed  a  second  up- 
right tuning-fork,  T,  also  furnished  with  a  mirror.  By 
the  horizontal  fork,  when  it  vibrates,  the  beam  is  tilted 
laterally;  by  the  vertical  fork,  vertically.  At  the  pres- 
ent moment  both  forks  are  motionless,  the  beam  of  light 
being  reflected  from  the  mirror  of  the  horizontal  to  that 
of  the  vertical  fork,  and  from  the  latter  to  the  screen,  on 
which  it  prints  a  brilliant  disk.  I  now  agitate  the  up- 
right fork,  leaving  the  other  motionless.  The  disk  is 
drawn  out  into  a  fine  luminous  band,  3  feet  long.  On 
sounding  the  second  fork,  the  straight  band  is  instantly 
transformed  into  a  white  ring  o  p,  Fig.  172,  36  inches 
in  diameter.  What  have  we  done  here?  Exactly  what 
we  did  in  our  first  experiment  with  the  pendulum.  We 
have  caused  a  beam  of  light  to  vibrate  simultaneously  in 
two  directions,  and  have  accidentally  hit  upon  the  phase 
when  one  fork  has  just  reached  the  limit  of  its  swing, 
and  come  momentarily  to  rest,  while  the  beam  is  receiving 
the  maximum  impulse  from  the  other  fork. 

That  the  circle  was  obtained  is,  as  stated,  a  mere 
accident;  but  it  was  a  fortunate  accident,  as  it  enables 
us  to  see  the  exact  similarity  between  the  motion  of  the 
beam  and  that  of  the  pendulum.  I  stop  both  forks,  and, 
agitating  them  afresh,  obtain  an  ellipse  with  its  axis 
oblique.  After  a  few  trials  we  obtain  the  straight  line, 
indicating  that  both  the  forks  then  pass  simultaneously 
through  their  positions  of  equilibrium.  In  this  way,  by 
combining  the  vibrations  of  the  two  forks,  we  reproduce 
all  the  figures  obtained  with  the  pendulum. 

When  the  vibrations  of  the  two  forks  are,  in  all  re- 
spects, absolutely  alike,  whatever  the  figure  may  be  which 
is  first  traced  upon  the  screen,  it  remains  unchanged  in 
form,  diminishing  only  in  size  as  the  motion  is  expended. 
But  the  slightest  difference  in  the  rates  of  vibration  de- 


412  SOUND. 

stroys  this  fixity  of  the  image.  I  endeavored  before  the 
lecture  to  render  the  unison  between  these  two  forks  as 
perfect  as  possible,  and  hence  you  have  observed  very 
little  alteration  in  the  shape  of  the  figure.  But  by 
moving  a  small  weight  along  the  prong  of  either  fork,  or 
by  attaching  to  either  of  them  a  bit  of  wax,  the  unison  is 
impaired.  The  figure  then  obtained  by  the  combination 
of  both  passes  slowly  from  a  straight  line  into  an  oblique 
ellipse,  thence  into  a  circle;  after  which  it  narrows  again 
to  an  ellipse  with  an  opposed  obliquity;  it  then  passes 
again  into  a  straight  line,  the  direction  of  which  is  at  right 
angles  to  the  first  direction.  Finally,  it  passes,  in  the 
reverse  order,  through  the  same  series  of  figures  to  the 
straight  line  with  which  we  began.  The  interval  be- 
tween two  successive  identical  figures  is  the  time  in 
which  one  of  the  forks  succeeds  in  executing  one  com- 
plete vibration  more  than  the  other.  Loading  the  fork 
still  more  heavily,  we  have  more  rapid  changes;  the 
straight  line,  ellipse,  and  circle,  being  passed  through  in 
quick  succession.  At  times  the  luminous  curve  exhibits 
a  stereoscopic  depth,  which  renders  it  difficult  to  believe 
that  we  are  not  looking  at  a  solid  ring  of  white-hot  metal. 
By  causing  the  mirror  of  the  fork,  T,  to  rotate  through 
a  small  arc,  the  steady  circle  first  obtained  is  drawn  out 
into  a  luminous  scroll  stretching  right  across  the  screen, 
Fig.  173.  The  same  experiment  made  with  the  changing 
FIG.  173. 


figure,  obtained  by  throwing  the  forks  out  of  unison, 
gives  us  a  scroll  of  irregular  amplitude,  Fig.  174.1 

We  have  next  to  combine  the  vibrations  of  two  forks, 
1  This  figure  corresponds  to  the  interval  15  : 10.     For  it  and  some 
other  figures,  I  am  indebted  to  that  excellent  mechanician,  M.  Konig, 
of  Paris. 


MUSICAL  INTERVALS  OPTICALLY  ILLUSTRATED.    413 

one  of  which  oscillates  with  twice  the  rapidity  of  the 
other;  in  other  words,  to  determine  the  figure  correspond- 


FIG.  174. 


FIG.  175. 


ing  to  the  combination  of  a  note  and  its  octave.  To  pre- 
pare ourselves  for  the  mechanics  of  the  problem,  we  must 
resort  once  more  to  our  pendulum;  for  it  also  can  be 
caused  to  oscillate  in  one  direction  twice  as  rapidly  as  in 
another.  By  a  complicated  mechanical  arrangement  this 
might  be  done  in  a  very  perfect  manner,  but  at  present 
simplicity  is  preferable  to  completeness.  The  wire  of  our 
pendulum  is  therefore  permitted  to 
descend  from  its  point  of  suspen- 
sion, A,  Fig.  175,  midway  between 
two  horizontal  glass  rods,  a  6,  a'  &', 
supported  firmly  at  their  ends,  and 
about  an  inch  asunder.  The  rods 
cross  the  wire  at  a  height  of  7  feet 
above  the  bob  of  the  pendulum. 
The  whole  length  of  the  pendulum 
being  28  feet,  the  glass  rods  inter- 
cept one-fourth  of  this  length.  On 
drawing  the  pendulum  aside  in  the 
direction  of  the  rods,  a  &,  a'  &',  and 
letting  it  go,  it  oscillates  freely  be- 
tween them.  I  bring  it  to  rest  and 
draw  it  aside  in  a  direction  perpen- 
dicular to  the  last;  a  length  of  7 
feet  only  can  now  oscillate,  and  by 
the  laws  of  oscillation  a  pendulum  7 
feet  long  vibrates  with  twice  the 
rapidity  of  a  pendulum  28  feet  long. 
I  wish  to  show  you  the  figure 


414  SOUND. 

described  by  the  combination  of  these  two  rates  of  vibra- 
tion. Attached  to  the  copper  ball,  p,  is  a  camel's-hair  pen- 
cil, intended  to  rub  lightly  upon  a  glass  plate  placed  on 
black  paper,  and  over  which  is  strewed  white  sand.  Al- 
lowing the  pendulum  to  oscillate  as  a  whole,  the  sand  is 
rubbed  away  along  a  straight  line  which  represents  the 
amplitude  of  the  vibration.  Let  a  &,  Fig.  176,  represent 
this  line,  which,  as  before,  we  will  assume  to  be  described 
FIG.  176.  in  one  second.  When  the  pendulum  is 

at  the  limit,  &,  of  its  swing,  let  a  rectan- 
gular impulse  be  imparted  to  it  suffi- 

ai .V  .J6  cient  to  carry  it  to  c  in  one-fourth  of  a 

second.  If  this  were  the  only  impulse 
acting  on  the  pendulum,  the  bob  would 
reach  c  and  return  to  b  in  half  a  second.  But  under  the 
actual  circumstances  it  is  also  urged  toward  d,  which 
point,  through  the  vibration  of  the  whole  pendulum,  it 
ought  also  to  reach  in  half  a  second.  Both  vibrations, 
therefore,  require  that  the  bob  shall  reach  d  at  the  same 
moment;  and  to  do  this  it  will  have  to  describe  the  curve 
b  c'  d.  Again,  in  the  time  required  by  the  long  pen- 
dulum to  pass  from  d  to  a,  the  short  pendulum  will  pass 
to  and  fro  over  the  half  of  its  excursion;  both  vibrations 
must  therefore  reach  a  at  the  same  moment,  and  to  ac- 
complish this  the  pendulum  describes  the  lower  curve 
between  d  and  a.  It  is  manifest  that  these  two  curves 
will  repeat  themselves  at  the  opposite  sides  of  a  &,  the 
combination  of  both  vibrations  producing  finally  a  figure 
of  8,  which  you  now.  see  fairly  drawn  upon  the  sand  be- 
fore you. 

The  same  figure  is  obtained  if  the  rectangular  impulse 
be  imparted  when  the  pendulum  is  passing  its  position  of 
rest,  d. 

I  have  here  supposed  the  time  occupied  by  the  pen- 
dulum in  describing  the  line  a  &  to  be  one  second.  Let 


COMBINATION  OF  A  NOTE  AND  ITS  OCTAVE.     415 

us  suppose  three-fourths  of  the  second  exhausted,  and 
the  pendulum  at  d',  Fig.  177,  in  its  excursion  toward  ~b> 
let  the  rectangular  impulse  then  be 
imparted  to  it,  sufficient  to  carry  it  to 
c  in  one-fourth  of  a  second.  Xow  the 
long  pendulum  requires  that  it  should 
move  from  d'  to  b  in  one-fourth  of  a 
second;  both  impulses  are  therefore 
satisfied  by  the  pendulum  taking  up 
the  position  c'  at  the  end  of  a  quarter  of  a  second.  To 
reach  this  position  it  must  describe  the  curve  d'  c'.  It 
will  manifestly  return  along  the  same  curve,  and  at  the 
end  of  another  quarter  of  a  second  find  itself  again  at  d'. 
From  d'  to  d  the  long  pendulum  requires  a  quarter  of  a 
second.  But  at  the  end  of  this  time  the  short  pendulum 
must  be  at  the  lower  limit  of  its  swing:  both  require- 
ments are  satisfied  by  the  pendulum  being  at  e.  We 
thus  obtain  one  arm,  c'  e,  of  a  curve  which  repeats  itself 
to  the  left  of  e;  so  that  the  entire  curve,  due  to  the 
combination  of  the  two  vibrations,  is  that  represented  in 
Fig.  165.  This  figure  is  a  parabola,  whereas  the  figure  of 
8  before  obtained  is  a  lemniscata. 

We  have  here  supposed  that,  at  the  moment  when 
the  rectangular  impulse  was  applied,  the  motion  of  the 
pendulum  was  toward  b:  if  it  were  pIQ 

toward   a,    we   should   obtain   the   in- 
verted  parabola,  as  shown  in  Fig.  178. 

Supposing,  finally,  the  impulse  to  a 
be  applied,  not  when  the  pendulum  is 
passing  through   its   position  of  equi-  .., 

librium,  nor  when  it  is  passing  a  point 
corresponding  to  three-fourths  or  one-fourth  of  the  time 
of  its  excursion,  but  at  some  other  point  in  the  line,  a  b, 
between  its  end  and  centre.  Under  these  circumstances 
\ve  should  have  neither  the  parabola  nor  the  perfectly 
symmetrical  figure  of  8  but  a  distorted  8. 

27 


416  SOUND. 

And  now  we  are  prepared  to  witness  with  profit  the 
combined  vibration  of  our  two  tuning-forks,  one  of  which 
sounds  the  octave  of  the  other.  Permitting  the  vertical 
fork,  T,  Fig.  172,  to  remain  undisturbed  in  front  of  the 
lamp,  we  can  oppose  to  it  an  horizontal  fork,  which 
vibrates  with  twice  the  rapidity.  The  first  passage  of 
the  bow  across  the  two  forks  reveals  the  exact  simi- 
larity of  this  combination,  and  that  of  our  pendulum.  A 
very  perfect  figure  of  8  is  described  upon  the  screen. 
Before  the  lecture  the  vibrations  of  these  two  forks  were 
fixed  as  nearly  as  possible  to  the  ratio  of  1  :  2,  and  the 
steadiness  of  the  figure  indicates  the  perfection  of  the 
tuning.  Stopping  both  forks,  and  again  agitating  them, 
we  have  the  distorted  8  upon  the  screen.  A  few  trials 
enable  me  to  bring  out  the  parabola.  In  all  these  cases 
the  figure  remains  fixed  upon  the  screen.  But  if  a 
morsel  of  wax  be  attached  to  one  of  the  forks,  the 
figure  is  steady  no  longer,  but  passes  from  the  perfect  8 
into  the  distorted  one,  thence  into  the  parabola,  from 
which  it  afterward  opens  out  to  an  8  once  more.  By 
augmenting  the  discord,  we  can  render  those  changes  as 
rapid  as  we  please. 

When  the  8  is  steady  on  the  screen,  a  rotation  of  the 
mirror  of  the  fork,  T,  produces  the  scroll  shown  in  Fig. 
179. 

FIG.  179. 


Our  next  combination  will  be  that  of  two  forks  vibrat- 
ing in  the  ratio  of  2  :  3.  Observe  the  admirable  steadi- 
ness of  the  figure  produced  by  the  compounding  of  these 
two  rates  of  vibration.  On  attaching  a  fourpenny-piece 
with  wax  to  one  of  the  forks  the  steadiness  ceases,  and  we 


OTHER  COMBINATIONS.  417 

have  an  apparent  rocking  to  and  fro  of  the  luminous 
figure.  Passing  on  to  intervals  of  3  :  4,  4  :  5,  and  5  :  6, 
the  figures  become  more  intricate  as  we  proceed.  The  last 
combination,  5  :  6,  is  so  entangled,  that  to  see  the  figure 
plainly  a  very  narrow  band  of  light  must  be  employed. 
The  distance  existing  between  the  forks  and  the  screen 
also  helps  us  to  unravel  the  complication. 

And  here  it  is  worth  noting  that,  when  the  figure  is 
fully  developed,  the  loops  along  the  vertical  and  horizontal 
edges  express  the  ratio  of  the  combined  vibrations.  In  the 
octave,  for  example,  we  have  two  loops  in  one  direction, 
and  one  in  another;  in  the  fifth,  two  loops  in  one  direc- 
tion, and  three  in  another.  When  the  combination  is  as 
1  :  3,  the  luminous  loops  are  also  as  1  :  3.  The  changes 
which  some  of  these  figures  undergo,  when  the  tuning  is 
not  perfect,  are  extremely  remarkable.  In  the  case  of 
1:3,  for  example,  it  is  difficult  at  times  not  to  believe 
that  you  are  looking  at  a  solid  link  of  white-hot  metal. 
The  figure  exhibits  a  depth,  apparently  incompatible  with 
its  being  traced  upon  a  plane  surface. 

Fig.  181  is  a  diagram  of  these  beautiful  figures,  includ- 
ing combinations  from  1  :  1  to  5  :  6.  In  each  case,  the 
characteristic  phases  of  the  vibration  are  shown;  and 
through  all  of  these  each  figure  passes  when  the  interval 
between  the  two  forks  is  not  pure.  I  also  add  here,  Fig. 
180,  two  phases  of  the  combination  8  :  9. 

FIG.  180. 


To  these  illustrations  of  rectangular  vibrations  I  add 
two  others,  Figs.  182  and  183,  from  a  very  beautiful  series 


418 


RECTANGULAR  VIBRATIONS.  419 


FIG.  182.    1 : 2. 


FIG.  183.    1:8. 


FIG.  184.    2:8.  FIG.  185.    8:4. 


420  SOUND. 

obtained  by  Mr.  Hubert  Airy  with  a  compound  pendulum. 
The  experiments  are  described  in  Nature  for  August  17 
and  September  7,  1871.  As  their  loops  indicate,  the 
figures  are  those  of  an  octave,  and  a  twelfth. 

But  the  most  instructive  apparatus  for  the  compound- 
ing of  rectangular  vibrations  is  that  of  Mr.  Tisley.  Tigs. 
184  and  185  are  copies  of  figures  obtained  by  him  through 
the  joint  action  of  two  distinct  pendulums;  the  rates  of 
vibration  corresponding  to  these  particular  figures  being 
2  :  3  and  3  :  4  respectively.  The  pen  which  traces  the 
figures  is  moved  simultaneously  by  two  rods  attached  to 
the  pendulums  above  their  places  of  suspension.  These 
two  rods  lie  in  the  two  planes  of  vibration,  being  at  right 
angles  to  the  pendulums,  and  to  each  other.  At  their 
place  of  intersection  is  the  pen.  By  means  of  a  ball  and 
socket,  of  a  special  kind,  the  rods  are  enabled  to  move 
with  a  minimum  of  friction  in  all  directions,  while  the 
rates  of  vibration  are  altered,  in  a  moment,  by  the  shift- 
ing of  movable  weights.  The  figures  are  drawn  either 
with  ink  on  paper,  or,  when  projection  on  a  screen  is  de- 
sired, by  a  sharp  point  on  smoked  glass.  When  the  pen- 
dulums, having  gone  through  the  entire  figure,  return  to 
their  starting-point,  they  have  lost  a  little  in  amplitude. 
The  second  excursion  will,  therefore,  be  smaller  than  the 
first,  and  the  third  smaller  than  the  second.  Hence  the 
series  of  fine  lines,  inclosing  gradually-diminishing  areas, 
shown  in  these  exquisite  figures.1  Mr.  Tisley's  apparatus 
reflects  the  highest  credit  upon  its  able  constructor. 

Sir  Charles  Wheatstone  devised,  many  years  ago,  a 
small  and  very  efficient  apparatus  for  the  compounding  of 
rectangular  vibrations.  A  drawing,  Fig.  186,  and  a  de- 
scription of  this  beautiful  little  instrument,  for  both  of 
which  I  am  indebted  to  its  eminent  inventor,  may  find  a 

1  For  some  beautiful  figures  of  this  description  I  am  indebted  to 
Prof.  Lyman,  of  Yale  College. 


WHEATSTONE'S  APPARATUS.  421 

place  here:  a  is  a  steel  rod  polished  at  its  upper  end  so 
as  to  reflect  a  point  of  light;  this  rod  moves  in  a  ball- 

FIG.  186. 


and-socket  joint  at  b,  so  that  it  may  assume  any  position. 
Its  lower  end  is  connected  with  two  arms  c  and  d,  placed 
at  right  angles  to  each  other,  the  other  ends  of  which 
are  respectively  attached  to  the  circumferences  of  the  two 
circular  disks  e  and  /.  The  axis  of  the  disk  e  carries  at 
its  opposite  end  another  larger  disk  g,  which  gives  motion 
to  the  small  disk  7i,  placed  on  the  axis  which  carries  the 
disk  /;  and  according  as  this  small  disk  li  is  placed  nearer 
to  or  farther  from  the  centre  of  the  disk  g,  it  communicates 
a  different  relative  motion  to  the  disk  /.  The  nut  and 
screw  i  enable  the  disk  Ti  to  be  placed  in  any  position 
between  the  centre  and  circumference  of  the  larger  disk  g, 
and  by  means  of  the  fork  j  the  disk  /  is  caused  to  revolve, 
whatever  may  be  the  position  of  the  disk  h.  By  this 
arrangement,  while  the  wheel  k  is  turned  regularly,  the 
rod  a  is  moved  backward  and  forward  by  the  disk  e  in  one 
direction,  and  by  the  disk  /,  with  any  relative  oscillatory 


422  SOUND. 

motion,  in  the  rectangular  direction.  The  end  of  the  rod 
is  thus  made  to  describe  and  to  exhibit  optically  all  the 
beautiful  acoustical  figures  produced  by  the  composition 
of  vibrations  of  different  periods  in  directions  rectangular 
to  each  other.  A  lever,  I,  bearing  against  the  nut  i,  indi- 
cates, on  a  scale  ra,  the  numerical  ratio  of  the  two  vibra- 
tions.1 

I  close  these  remarks  on  the  combination  of  rectan- 
gular vibrations  with  a  brief  reference  to  an  apparatus 
constructed  by  Mr.  A.  E.  Donkin,  of  Exeter  College, 
Oxford,  and  described  in  the  "  Proceedings  of  the  Royal 
Society,"  vol.  xxii.,  p.  196.  In  its  construction  great 
mechanical  knowledge  is  associated  with  consummate 
skill.  I  saw  the  apparatus  as  a  wooden  model,  before 
it  quitted  the  hands  of  its  inventor,  and  was  charmed 
with  its  performance.  It  is  now  constructed  by  Messrs. 
Tisley  and  Spiller. 

1  Mr.  Sang,  of  Edinburgh,  was,  I  believe,  the  first  to  treat  this  sub- 
ject analytically. 


SUMMARY.  423 


SUMMAKY  OF  CHAPTER  IX. 

BY  the  division  of  a  string  Pythagoras  determined 
the  consonant  intervals  in  music,  proving  that,  the  simpler 
the  ratio  of  the  two  parts  into  which  the  string  was  divided, 
the  more  perfect  is  the  harmony  of  the  sounds  emitted 
by  the  two  parts  of  the  string.  Subsequent  investigators 
showed  that  the  strings  act  thus  because  of  the  relation  of 
their  lengths  to  their  rates  of  vibration. 

With  the  double  siren  this  law  of  consonance  is  readily 
illustrated.  Here  the  most  perfect  harmony  is  the  unison, 
where  the  vibrations  are  in  the  ratio  of  1  :  1.  ^ext  comes 
the  octave,  where  the  vibrations  are  in  the  ratio  of  1  :  2. 
Afterward  follow  in  succession  the  fifth,  with  a  ratio  of 
2:3;  the  fourth,  with  a  ratio  of  3  :  4 ;  the  major  third, 
with  a  ratio  of  4  :  5;  and  the  minor  third,  with  a  ratio  of 
5  :  6.  The  interval  of  a  tone,  represented  by  the  ratio 
8  :  9,  is  dissonant,  while  that  of  a  semi-tone,  with  a  ratio 
of  15  :  16,  is  a  harsh  and  grating  dissonance. 

The  musical  interval  is  independent  of  the  absolute 
number  of  the  vibrations  of  the  two  notes,  depending  only 
on  the  ratio  of  the  two  rates  of  vibration. 

The  Pythagoreans  referred  the  pleasing  effect  of  the 
consonant  intervals  to  number  and  harmony,  and  con- 
nected them  with  "  the  music  of  the  spheres."  Euler  ex- 
plained the  consonant  intervals  by  reference  to  the  consti- 
tution of  the  mind,  which,  he  affirmed,  took  pleasure  in 
simple  calculations.  The  mind  was  fond  of  order,  but 
of  such  order  as  involved  no  weariness  in  its  contempla- 


424:  SOUND. 

tion.  This  pleasure  was  afforded  by  the  simpler  ratios 
in  the  case  of  music. 

The  researches  of  Helmholtz  prove  the  rapid  succes- 
sion of  beats  to  be  the  real  cause  of  dissonance  in  music. 

By  means  of  two  singing-flames,  the  pitch  of  one  of 
them  being  changeable  by  the  telescopic  lengthening  of 
its  tube,  beats  of  any  degree  of  slowness  or  rapidity 
may  be  produced.  Commencing  with  beats  slow  enough 
to  be  counted,  and  gradually  increasing  their  rapidity,  we 
reach,  without  breach  of  continuity,  downright  disso- 
nance. 

But,  to  grasp  this  theory  in  all  its  completeness,  we 
must  refer  to  the  constitution  of  the  human  ear.  AVe 
have  first  the  tympanic  membrane,  which  is  the  anterior 
boundary  of  the  drum  of  the  ear.  Across  the  drum 
stretches  a  series  of  little  bones,  called  respectively  the 
hammer,  the  anvil,  and  the  stirrup-bone;  the  latter 
abutting  against  a  second  membrane,  which  forms  part  of 
the  posterior  boundary  of  the  drum.  Beyond  this  mem- 
brane is  the  labyrinth  filled  with  water,  and  having  its 
lining  membrane  covered  with  the  filaments  of  the  audi- 
tory nerve. 

Every  shock  received  by  the  tympanic  membrane  is 
transmitted  through  the  series  of  bones  to  the  opposite 
membrane;  thence  to  the  water  of  the  labyrinth,  and 
thence  to  the  auditory  nerve. 

The  transmission  is  not  direct.  The  vibrations  are  in 
the  first  place  taken  up  by  certain  bodies,  which  can  swing 
sympathetically  with  them.  These  bodies  are  of  three 
kinds:  the  otolites,  which  are  little  crystalline  particles; 
the  bristles  of  Max  Schultze;  and  the  fibres  of  Corti's 
organ.  This  latter  is  to  all  intents  and  purposes  a  stringed 
instrument,  of  extraordinary  complexity  and  perfection, 
placed  within  the  ear. 

As  regards  our  present  subject,  the  strings  of  Corti's 


SUMMARY.  425 

organ  probably  play  an  especially  important  part.  That 
one  string  should  respond,  in  some  measure,  to  another,  it 
is  not  necessary  that  the  unison  should  be  perfect;  a  cer- 
tain degree  of  response  occurs  in  the  immediate  neighbor- 
hood of  unison. 

Hence  each  of  two  strings,  not  far  removed  from  each 
other  in  pitch,  can  cause  a  third  string,  of  intermediate 
pitch,  to  respond  sympathetically.  And  if  the  two  strings 
be  sounded  together,  the  beats  which  they  produce  are 
propagated  to  the  intermediate  string. 

So,  as  regards  Corti's  organ,  when  single  sounds  of 
various  pitches,  or  rather  when  vibrations  of  various  ra- 
pidities, fall  upon  its  strings,  the  vibrations  are  responded 
to  by  the  particular  string  whose  period  coincides  with 
theirs.  And  when  two  sounds,  close  to  each  other  in 
pitch,  produce  beats,  the  intermediate  Corti's  fibre  is  acted 
on  by  both,  and  .responds  to  the  beats. 

In  the  middle  and  upper  portions  of  the  musical  scale 
the  beats  are  most  grating  and  harsh  when  they  succeed 
each  other  at  the  rate  of  33  per  second.  When  they 
occur  at  the  rate  of  132  per  second,  they  cease  to  be 
sensible. 

The  perfect  consonance  of  certain  musical  intervals 
is  due  to  the  absence  of  beats.  The  imperfect  consonance 
of  other  intervals  is  due  to  their  existence.  And  here 
the  overtones  play  a  part  of  the  utmost  importance.  For, 
though  the  primaries  may  sound  together  without  any 
perceptible  roughness,  the  overtones  may  be  so  related  to 
each  other  as  to  produce  harsh  and  grating  beats.  A 
strict  analysis  of  the  subject  proves  that  intervals  which 
require  large  numbers  to  express  them,  are  invariably 
accompanied  by  overtones  which  produce  beats;  while  in 
intervals  expressed  by  small  numbers  the  beats  are  prac- 
tically absent. 

The  graphic  representation  of  the  consonances  and  dis- 


426  SOUND. 

sonances  of  the  musical  scale,  by  Helmholtz,  furnishes  a 
striking  proof  of  this  explanation. 

The  optical  illustration  of  the  musical  intervals  has 
been  effected  in  a  very  beautiful  manner  by  Lissajous. 
Corresponding  to  each  interval  is  a  definite  figure,  pro- 
duced by  the  combination  of  its  vibrations. 

The  compounding  of  vibrations  has,  of  late  years,  been 
beautifully  illustrated  by  apparatus  constructed  by  Sir  C. 
"Wheatstone,  Mr.  Herbert  Airy,  and  Mr.  A.  E.  Donkin; 
and  by  the  beautiful  pendulum  apparatus  of  Mr.  Tisley, 
of  the  firm  of  Tisley  and  Spiller. 

The  pressure  which,  on  a  former  occasion,  prevented 
me  from  adding  a  "  summary  "  to  this  chapter,  was  also 
the  cause  of  hastiness,  and  partial  inaccuracy,  in  its  sketch 
of  the  theory  of  Helmholtz.  That  the  sketch  needed 
emendation  I  have  long  known,  but  I  did  not  think  it 
worth  while  to  anticipate  the  correction  here  made;  as 
the  chapter,  imperfect  as  it  was,  had  been  published,  with- 
out comment,  in  Germany,  by  Helmholtz  himself. 


APPENDICES. 


APPENDIX    I. 

ON  THE  INFLUENCE  O7  MUSICAL  SOUNDS  ON  THE  FLAME  OF  A  JET  OF 
COAL-GAS.       BY  JOHN  LE  CONTE,   M.   D.1 

A  SHORT  time  after  reading  Prof.  John  Tyndall's  excellent  article 
"On  the  Sounds  produced  by  the  Combustion  of  Gases  in  Tubes,"  a 
I  happened  to  be  one  of  a  party  of  eight  persons  assembled  after  tea 
for  the  purpose  of  enjoying  a  private  musical  entertainment.  Three 
instruments  were  employed  in  the  performance  of  several  of  the 
grand  trios  of  Beethoven,  namely,  the  piano,  violin,  and  violoncello. 
Two  "fish-tail"  gas-burners  projected  from  the  brick  wall  near  the 
piano.  Both  of  them  burned  with  remarkable  steadiness,  the  win- 
dows being  closed  and  the  air  of  the  room  being  very  calm.  Never- 
theless, it  was  evident  that  one  of  them  was  under  a  pressure  nearly 
sufficient  to  make  \i  flare. 

Soon  after  the  music  commenced,  I  observed  that  the  flame  of 
the  last-mentioned  burner  exhibited  pulsations  in  height  which  were 
exactly  synchronous  with  the  audible  beats.  This  phenomenon  was 
very  striking  to  every  one  in  the  room,  and  especially  so  when  the 
strong  notes  of  the  violoncello  came  in.  It  was  exceedingly  inter- 
esting to  observe  how  perfectly  even  the  trills  of  this  instrument 
were  reflected  on  the  sheet  of  flame.  A  deaf  man  might  have  seen  the 
harmony.  As  the  evening  advanced,  and  the  diminished  consump- 
tion of  gas  in  the  city  increased  the  pressure,  the  phenomenon  became 
more  conspicuous.  The  jumping  of  the  flame  gradually  increased, 
became  somewhat  irregular,  and  finally  it  began  to  flare  continuous- 
ly, emitting  the  characteristic  sound  indicating  the  escape  of  a  greater 

1  This  able  paper  was  the  starting-point  of  the  experiments  on 
sensitive  flames,  recordel  in  Chapters  VI.  and  VII.;  the  researches  of 
Thomas  Young  and  Savart  beinc:  the  starting-point  of  the  experiments 
on  smoke-jets  and  water-jets. — J.  T. 

*  Philosophical  Magazine,  section  4,  vol.  xiii.,  p.  473,  1857. 
427 


428  APPENDIX. 

amount  of  gas  than  could  be  properly  consumed.  I  then  ascertained 
by  experiment  that  the  phenomenon  did  not  take  place  unless  the 
discharge  of  gas  was  so  regulated  that  the  flame  approximated  to  the 
condition  oi  flaring.  I  likewise  determined  by  experiment  that  the 
effects  were  not  produced  by  jarring  or  shaking  the  floor  and  walls  of 
the  room  by  means  of  repeated  concussions.  Hence  it  is  obvious 
that  the  pulsations  of  the  flame  were  not  owing  to  indirect  vibrations 
propagated  through  the  medium  of  the  walls  of  the  room  to  the 
burning  apparatus,  but  must  have  been  produced  by  the  direct  influ- 
ence of  the  aerial  sonorous  pulses  on  the  burning  jet. 

In  the  experiments  of  M.  Schaffgotsch  and  Prof.  J.  Tyndall,  it  is 
evident  that  "the  shaking  of  the  singing-flame  within  the  glass 
tube,"  produced  by  the  voice  or  the  siren,  was  a  phenomenon  per- 
fectly analogous  to  what  took  place  under  my  observation  without 
the  intervention  of  a  tube.  In  my  case  the  discharge  of  gas  was  so 
regulated  that  there  was  a  tendency  in  the  flame  to  flare,  or  to  emit 
a  "  ringing-sound."  Under  these  circumstances,  strong  aerial  pulsa- 
tions occurring  at  regular  intervals  were  sufficient  to  develop  syn- 
chronous fluctuations  in  the  height  of  the  flame.  It  is  probable  that 
the  effects  would  be  more  striking  when  the  tones  of  the  musical 
instrument  are  nearly  in  unison  with  the  sounds  which  would  be 
produced  by  the  flame  under  the  slight  increase  in  the  rapidity  of 
discharge  of  gas  required  to  manifest  the  phenomenon  of  flaring. 
This  point  might  be  submitted  to  an  experimental  test. 

As  in  Prof.  Tyndall's  experiments  on  the  jet  of  gas  burning  within 
a  tube,  clapping  of  the  hands,  shouting,  etc.,  were  ineffectual  in  con- 
verting the  "silent  "  into  the  "singing-flame,"  so  in  the  case  under 
consideration,  irregular  sounds  did  not  produce  any  perceptible  influ- 
ence. It  seems  to  be  necessary  that  the  impulses  should  accumulate, 
in  order  to  exercise  an  appreciable  effect. 

"With  regard  to  the  mode  in  which  the  sounds  are  produced  by 
the  combustion  of  gases  in  tubes,  it  is  universally  admitted  that  the 
explanation  given  by  Prof.  Faraday  in  1818  is  essentially  correct. 
It  is  well  known  that  he  referred  these  sounds  to  the  successive 
explosions  produced  by  the  periodic  combination  of  the  atmospheric 
oxygen  with  the  issuing  jet  of  gas.  While  reading  Prof.  J.  Plateau's 
admirable  researches  (third  series)  on  the  "Theory  of  the  Modifica- 
tions experienced  by  Jets  of  Liquid  issuing  from  Circular  Orifices 
when  exposed  to  the  Influence  of  Vibratory  Motions,"1  the  idea 
flashed  across  my  mind  that  the  phenomenon  which  had  fallen  under 

1  Philosophical  Magazine,  section  4,  vol.  xiv.,  p.  1,  et  seq.,  July,  1857. 


APPENDIX.  429 

my  observation  was  nothing  more  than  a  particular  case  of  the 
etfects  of  sounds  on  all  kinds  of  fluid  jets.  Subsequent  reflection 
has  only  served  to  fortify  this  first  impression. 

The  beautiful  investigations  of  Felix  Savart  on  the  influence  of 
sounds  on  jets  of  water  afford  results  presenting  so  many  points  of 
analogy  with  their  effects  on  the  jet  of  burning  gas,  that  it  may  be 
well  to  inquire  whether  both  of  them  may  be  referred  to  a  common 
cause.  In  order  to  place  this  in  a  striking  light,  I  shall  subjoin  some 
of  the  results  of  Savurt's  experiments.  Vertically-descending  jets  of 
water  receive  the  following  modifications  under  the  influence  of 
vibrations : 

1.  The  continuous  portions  become  shortened;  the  vein  resolves 
itself  into  separate  drops  nearer  the  orifice  than  when  not  under  the 
influence  of  vibrations. 

2.  Each  of  the  masses,  as  they  detach  themselves  from  the  ex- 
tremity of  the  continuous  part,  becomes  flattened  alternately  in  a 
vertical  and  horizontal  direction,  presenting  to  the  eye,  under  the 
influence  of  their   translatory  motion,  regularly-disposed  series  of 
maxima  and  minima  of  thickness,  or  ventral  segments  and  nodes. 

3.  The  foregoing  modifications  become  much  more  developed  and 
regular  when  a  note,  in  unison  with  that  which  would  be  produced 
by  the  shock  of  the  discontinuous  part  of  the  jet  against  a  stretched 
membrane,  is  sounded  in  its  neighborhood.     The  continuous  part 
becomes  considerably  shortened,  and  the  ventral  segments  are  en- 
larged. 

4.  When  the  note  of  the  instrument  is  almost  in  unison,  the  con- 
tinuous part  of  the  jet  is  alternately  lengthened  and  shortened,  and 
the  beats  which  coincide  with  these  variations  in  length  can  be  rec- 
ognized by  the  ear. 

5.  Other  tones  act  with  less  energy  on  the  jet,  and  some  produce 
no  sensible  effect. 

When  a  jet  is  made  to  ascend  obliquely,  so  that  the  discontinuous 
part  appears  scattered  into  a  kind  of  sheaf  in  the  same  vertical 
plane,  M.  Savart  found : 

a.  That,   under  the  influence  of  vibrations  of  a   determinate 
period,  this  sheaf  may  form  itself  into  two  distinct  jets,  each  possess- 
ing regularly-disposed  ventral  segments  and  nodes;  sometimes  with 
a  different  node,  the  sheath  becomes  replaced  by  three  jets. 

b.  The  note  which  produces  the  greatest  shortening  of  the  con- 
tinuous part  always  reduces  the  whole  to  a  single  jet,  presenting  a 
perfectly  icgular  system  of  ventral  segments  and  nodes. 


430  APPENDIX. 

In  the  last  memoir  of  M.  Savart — a  posthumous  one,  presented  to 
the  Academy  of  Sciences  of  Paris,  by  M.  Arago,  in  1853  ' — several 
remarkable  acoustic  phenomena  are  noticed  in  relation  to  the  musical 
tones  produced  by  the  efflux  of  liquids  through  short  tubes.  When 
certain  precautions  and  conditions  are  observed  (which  are  minutely 
detailed  by  this  able  experimentalist),  the  discharge  of  the  liquid 
gives  rise  to  a  succession  of  musical  tones  of  great  intensity  and  of  a 
peculiar  quality,  somewhat  analogous  to  that  of  the  human  voice. 
That  these  notes  were  not  produced  by  the  descending  drops  of  the 
liquid  vein,  was  proved  by  permitting  it  to  discharge  itself  into  a 
vessel  of  water,  while  the  orifice  was  below  the  surface  of  the  latter. 
In  this  case  the  jet  of  liquid  must  have  been  continuous,  but  never- 
theless the  notes  were  produced.  These  unexpected  results  have 
been  entirely  confirmed  by  the  more  recent  experiments  of  Prof. 
Tyndall.2 

According  to  the  researches  of  M.  Plateau,  all  the  phenomena  of 
the  influence  of  vibrations  on  jets  of  liquid  are  referable  to  the  con- 
flict between  the  vibrations  and  the  forces  of  figure  ("  forces  Jigu- 
ratr ices'1'1).  If  the  physical  fact  is  admitted— and  it  seems  to  be 
indisputable — that  a  liquid  cylinder  attains  a  limit  of  stability  when 
the  proportion  between  its  length  and  its  diameter  is  in  the  ratio  of 
twenty-two  to  seven,  it  is  almost  a  physical  necessity  that  the  jet 
should  assume  the  constitution  indicated  by  the  observations  of 
Savart.  It  likewise  seems  highly  probable  that  a  liquid  jet,  while  in 
a  transition  stage  to  discontinuous  drops,  should  be  exceedingly  sen- 
sitive to  the  influence  of  all  kinds  of  vibrations.  It  must  be  con- 
fessed, however,  that  Plateau's  beautiful  and  coherent  theory  does 
not  appear  to  embrace  Savart 's  last  experiment,  in  which  the  musical 
tones  were  produced  by  a  jet  of  water  issuing  under  the  surface  of 
the  same  liquid.  It  is  rather  difficult  to  imagine  what  agency  the 
"  forces  of  figure  "  could  have,  under  such  circumstances,  in  the  pro- 
duction of  the  phenomenon.  This  curious  experiment  tends  to  cor- 
roborate Savart's  original  idea,  that  the  vibrations  which  produce 
the  sounds  must  take  place  in  the  glass  reservoir  itself,  and  that  the 
cause  must  be  inherent  in  the  phenomenon  of  the  flow. 

To  apply  the  principles  of  Plateau's  theory  to  gaseous  jets,  we 
are  compelled  to  abandon  the  idea  of  the  non-existence  of  molecular 
cohesion  in  gases.  But  is  there  not  abundant  evidence  to  show  that 

1  Comptes  Rendus  for  August,  1833.  Also  Philosophical  Magazine, 
section  4,  vol.  vii..  p.  180.  1854. 

8  Philosophical  Magazine,  section  4,  vol.  viii.,  p.  74.  1854. 


APPENDIX.  431 

cohesion  does  exist  among  the  particles  of  gaseous  masses  ?  Does  not 
the  deviation  from  rigorous  accuracy,  both  in  the  law  of  Mariotte 
and  Gay-Lussac — especially  in  the  case  of  condensable  gases,  as 
shown  by  the  admirable  experiments  of  M.  Regnault — clearly  prove 
that  the  hypothesis  of  the  non-existence  of  cohesion  in  aeriform 
bodies  is  fallacious  ?  Do  not  the  expanding  rings  which  ascend 
when  a  bubble  of  phosphuretted  hydrogen  takes  fire  in  the  air, 
indicate  the  existence  of  some  cohesive  force  in  the  gaseous  product 
of  combustion  (aqueous  vapor),  whose  outlines  are  marked  by  the 
opaque  phosphoric  acid  ?  In  short,  does  not  the  very  form  of  the 
flame  of  a  "fish-tail"  burner  demonstrate  that  cohesion  must  exist 
among  the  particles  of  the  issuing  gas  ?  It  is  well  known  that  in  this 
burner  the  single  jet  which  issues  is  formed  by  the  union  of  two 
oblique  jets  immediately  before  the  gas  is  emitted.  The  result  is  a 
perpendicular  sheet  of  flame.  How  is  such  a  result  produced  by  the 
mutual  action  of  two  jets,  unless  the  force  of  cohesion  is  brought 
into  play  ?  Is  it  not  obvious  that  such  a  fan-like  flame  must  be 
produced  by  the  same  causes  as  those  varied  and  beautiful  forms  of 
aqueous  sheets,  developed  by  the  mutual  action  of  jets  of  water,  so 
strikingly  exhibited  in  the  experiments  of  Savart  and  of  Magnus  ? 

If  it  be  granted  that  gases  possess  molecular  cohesion,  it  seems  to 
be  physically  certain  that  jets  of  gas  must  be  subject  to  the  same 
laws  as  those  of  liquid.  Vibratory  movements  excited  in  the  neigh- 
borhood ought,  therefore,  to  produce  modifications  in  them  analogous 
to  those  recorded  by  M.  Savart  in  relation  to  jets  of  water.  Flame 
or  incandescent  gas  presents  gaseous  matter  in  a  visible  form,  admi- 
rably adapted  for  experimental  investigation  ;  and,  when  produced  by 
a  jet,  should  be  amenable  to  the  principles  of  Plateau's  theory.  Ac- 
cording to  this  view,  the  pulsations  or  beats  which  I  observed  in  the 
gas-flame  when  under  the  influence  of  musical  sounds,  are  produced 
by  the  conflict  between  the  aerial  vibrations  and  the  "forces  of 
figure  "  (as  Plateau  calls  them)  giving  origin  to  periodical  fluctua- 
tions of  intensity,  depending  on  the  sonorous  pulses. 

If  this  view  is  correct,  will  it  not  be  necessary  for  us  to  modify 
our  ideas  in  relation  to  the  agency  of  tubes  in  developing  musical 
sounds  by  means  of  burning  jets  of  gas  ?  Must  we  not  look  upon 
all  burning  jets — as  in  the  case  of  water-jets — as  musically  inclined  ; 
and  that  the  use  of  tubes  merely  places  them  in  a  condition  favor- 
able for  developing  the  tones  ?  It  is  well  known  that  burning  jets 
frequently  emit  a  singing-sound  when  they  are  perfectly  free.  Are 
these  sounds  produced  by  successive  explosions  analogous  to  those 


432  APPENDIX. 

which  take  place  in  glass  tubes  ?  It  is  very  certain  that,  under  the 
influence  of  molecular  forces,  any  cause  which  tends  to  elongate  the 
flame,  without  effecting  the  velocity  of  discharge,  must  tend  to 
render  it  discontinuous,  and  thus  bring  about  that  mixture  of  gas 
and  air  which  is  essential  to  the  production  of  the  explosions.  The 
influence  of  tubes,  as  well  as  of  aerial  vibrations,  in  establishing  this 
condition  of  things,  is  sufficiently  obvious.  Was  not  the  "beaded 
line"  with  its  succession  of  "luminous  stars,"  which  Prof.  Tyndall 
observed  when  a  flame  of  olefiant  gas,  burning  in  a  tube,  was  ex- 
amined by  means  of  a  moving  mirror,  an  indication  that  the  flame 
became  discontinuous,  precisely  as  the  continuous  part  of  a  jet  of 
water  becomes  shortened,  and  resolved  into  isolated  drops,  under  the 
influence  of  sonorous  pulsations  ?  But  I  forbear  enlarging  on  this 
very  interesting  subject,  inasmuch  as  the  accomplished  physicist  last 
named  has  promised  to  examine  it  at  a  future  period.  In  the  hands 
of  so  sagacious  a  philospher,  we  may  anticipate  a  most  searching 
investigation  of  the  phenomena  in  all  their  relations.  In  the  mean 
time  I  wish  to  call  the  attention  of  men  of  science  to  the  view  pre- 
sented in  this  article,  in  so  far  as  it  groups  together  several  classes 
of  phenomena  under  one  head,  and  may  be  considered  a  partial  gen- 
eralization.— From  SILLIMAN'S  American  Journal  for  January,  1858. 


APPENDIX  II. 

ON   ACOUSTIC   REVERSIBILITY.1 

ON  the  21st  and  22d  of  June,  1822,  a  commission,  appointed  by 
the  Bureau  des  Longitudes  of  France,  executed  a  celebrated  series 
of  experiments  on  the  velocity  of  sound.  Two  stations  had  been 
chosen,  the  one  at  Villejuif,  the  other  at  Montlh6ry,  both  lying  south 
of  Paris,  and  11'6  miles  distant  from  each  other.  Prony,  Mathieu, 
and  Arago,  were  the  observers  at  Villejuif,  while  Humboldt,  Bouvard, 
and  Gay-Lussac  were  at  Montlhery.  Guns,  charged  sometimes  with 
two  pounds  and  sometimes  with  three  pounds  of  powder,  were  fired 
at  both  stations,  and  the  velocity  was  deduced  from  the  interval 
between  the  appearance  of  the  flash  and  the  arrival  of  the  sound. 

On  this  memorable  occasion  an  observation  was  made  which,  as 
far  as  I  know,  has  remained  a  scientific  enigma  to  the  present  hour. 
1  "  Proceedings  of  the  Royal  Institution,"  January  15,  1875. 


APPENDIX.  433 

It  was  noticed  that  while  every  report  of  the  cannon  fired  at  Mont- 
lhery was  heard  with  the  greatest  distinctness  at  Villejuif,  by  far 
the  greater  number  of  the  reports  from  Villejuif  failed  to  reach 
Montlhery.  Had  wind  existed,  and  had  it  blown  from  Montlhery  to 
Villejuif,  it  would  have  been  recognized  as  the  cause  of  the  observed 
difference  ;  but  the  air  at  the  time  was  calm,  the  slight  motion  of 
translation  actually  existing  being  from  Villejuif  towTard  Montlhery, 
or  against  the  direction  in  which  the  sound  was  best  heard. 

So  marked  was  the  difference  in  transmissive  power  between  the 
two  directions,  that  on  June  22d,  while  every  shot  fired  at  Montlhery 
was  heard  d  merveille  at  Villejuif,  but  one  shot  out  of  twelve  fired  at 
Villejuif  was  heard,  and  that  feebly,  at  the  other  station. 

With  the  caution  which  characterized  him  on  other  occasions, 
and  which  has  been  referred  to  admiringly  by  Faraday,1  Arago  made 
no  attempt  to  explain  this  anomaly.  His  words  are  :  "Quant  aux 
diff6rences  si  remarquables  d'intensit6  que  le  bruit  du  canon  a  tou- 
jours  presentees  suivant  qu'il  se  propageait  du  nord  au  sud  entre 
Villejuif  et  Montlhery,  ou  du  sud  au  nord  entre  cette  seconde  station 
et  la  premiere,  nous  ne  chercherons  pas  aujourd'hui  a  1'expliquer, 
parce  que  nous  ne  pourrions  offrir  au  lecteur  que  des  conjectures 
denuees  de  preuves." a 

I  have  tried,  after  much  perplexity  of  thought,  to  bring  this  sub- 
ject within  the  range  of  experiment,  and  have  now  to  submit  the 
following  solution  of  the  enigma  :  The  first  step  was  to  ascertain 
whether  the  sensitive  flame,  referred  to  in  my  recent  paper  in  the 
"Philosophical  Transactions,"  could  be  safely  employed  in  experi- 
ments on  the  mutual  reversibility  of  a  source  of  sound  and  an  object 
on  which  the  sound  impinges.  Now,  the  sensitive  flame  usually  em- 
ployed by  me  measures  from  eighteen  to  twenty-four  inches  in 
height,  while  the  reed  employed  as  a  source  of  sound  is  less  than  a 
square  quarter  of  an  inch  in  area.  If,  therefore,  the  whole  flame,  or 
the  pipe  which  fed  it,  were  sensitive  to  sonorous  vibrations,  strict . 
experiments  on  reversibility  with  the  reed  and  flame  might  be  diffi- 
cult, if  not  impossible.  Hence  my  desire  to  learn  whether  the  seat 
of  sensitiveness  was  so  localized  in  the  flame  as  to  render  the  con- 
templated interchange  of  flame  and  reed  permissible. 

The  flame  being  placed  behind  a  cardboard  screen,  the  shank  of 
a  funnel  passed  through  a  hole  in  the  cardboard  was  directed  upon 
the  middle  of  the  flame.    The  sound-waves  issuing  from  the  vibrating 
1  "  Researches  in  Chemistry  and  Physics,"  p.  484. 
8  "  Connaissance  des  Temps,"  1825,  p.  370. 


434:  APPENDIX. 

reed,  placed  within  the  funnel,  produced  no  sensible  effect  upon  the 
flame.  Shifting  the  funnel  so  as  to  direct  its  shank  upon  the  root  of 
the  flame,  the  action  was  violent. 

To  augment  the  precision  of  the  experiment,  the  funnel  was  con- 
nected with  a  glass  tube  three  feet  long  and  half  an  inch  in  diameter, 
the  object  being  to  weaken,  by  distance,  the  effect  of  the  waves  dif- 
fracted round  the  edge  of  the  funnel,  and  to  permit  those  only  which 
passed  through  the  glass  tube  to  act  upon  the  flame. 

Presenting  the  end  of  the  tube  to  the  orifice  of  the  burner 
(ft,  Fig.  1),  or  the  orifice  to  the  end  of  the  tube,  the  flame  was  vio- 
lently agitated  by  the  sounding-reed,  R.  On  shitting  the  tube,  or  the 
burner,  so  as  to  concentrate  the  sound  on  a  portion  of  the  flame  about 
half  an  inch  above  the  orifice,  the  action  was  nil.  Concentrating  the 
sound  upon  the  burner  itself,  about  half  an  inch  below  its  orifice, 
there  was  no  action. 

These  experiments  demonstrate  the  localization  of  "the  seat  of 
sensitiveness,"  and  they  prove  the  flame  to  be  an  appropriate  instru- 
ment for  the  contemplated  experiments  on  reversibility. 

FIG.  1. 


The  experiments  then  proceeded  thus:  The  sensitive  flame 
being  placed  close  behind  a  screen  of  cardboard  1 8  inches  high  by 
•  12  inches  wide,  a  vibrating  reed,  standing  at  the  same  height  as  the 
root  of  the  flame,  was  placed  at  a  distance  of  6  feet  on  the  other 
side  of  the  screen.  The  sound  of  the  reed,  in  this  position,  pro- 
duced a  strong  agitation  of  the  flame. 

The  whole  upper  half  of  the  flame  was  here  visible  from  the 
reed  ;  hence  the  necessity  of  the  foregoing  experiments  to  prove 
the  action  of  the  sound  on  the  upper  portion  of  the  flame  to  be 
nil,  and  that  the  waves  had  really  to  bend  round  the  edge  of  the 
screen,  so  as  to  reach  the  seat  of  sensitiveness  in  the  neighborhood 
of  the  burner. 


APPENDIX.  435 

The  positions  of  the  flame  and  reed  were  reversed,  the  latter 
being  now  close  behind  the  screen,  and  the  former  at  a  distance 
of  6  feet  from  it.  The  sonorous  vibrations  were  without  sensible 
action  upon  the  flame. 

The  experiment  was  repeated  and  varied  in  many  ways. 
Screens  of  various  sizes  were  employed  ;  and,  instead  of  reversing 
the  positions  of  the  flame  and  reed,  the  screen  itself  was  moved, 
so  as  to  bring,  in  some  experiments  the  flame,  and  in  other  experi- 
ments the  reed,  close  behind  it.  Care  was  also  taken  that  no 
reflected  sound  from  the  walls  or  ceiling  of  the  laboratory,  or 
from  the  body  of  the  experimenter,  should  have  anything  to  do 
with  the  effect.  In  all  cases  it  was  shown  that  the  sound  was  ef- 
fective when  the  reed  was  at  a  distance  from  the  screen,  and  the 
flame  close  behind  it ;  while  the  action  was  insensible  when  these 
positions  were  reversed. 

Thus,  let  s  e,  Fig.  2,  be  a  vertical  section  of  the  screen.  When 
the  reed  was  at  A  and  the  flame  at  B  there  was  no  action  ;  when 
the  reed  was  at  B  and  the  flame  at  A  the  action  was  decided.  It 
may  be  added  that  the  vibrations  communicated  to  the  screen 


itself,  and  from  it  to  the  air  beyond  it,  were  without  effect  ;  for 
when  the  reed,  which  at  B  was  effectual,  was  shifted  to  C,  where 
its  action  on  the  screen  was  greatly  augmented,  it  ceased  to  have 
any  action  on  the  flame  at  A. 

"We  are  now,  I  think,  prepared  to  consider  the  failure  of  re- 
versibility in  the  larger  experiments  of  1822.  Happily  an  inci- 
dental observation  of  great  significance  comes  here  to  our  aid. 
It  was  observed  and  recorded  at  the  time  that,  while  the  reports 
of  the  guns  at  Villejuif  were  without  echoes,  a  roll  of  echoes, 
lasting  from  20  to  25  seconds,  accompanied  every  shot  at 
Montlhery,  being  heard  by  the  observers  there.  Arago,  the 
writer  of  the  report,  referred  these  echoes  to  reflection  from  the 


436  APPENDIX. 

clouds,  an  explanation  which  I  think  we  are  now  entitled  to  regard 
as  problematical.  The  report  says  that  "tous  les  coups  tires  d 
Montlhery  y  etaient  accompagnes  d'un  roulement  semblable  a 
celui  du  tonnerre."  I  have  italicized  a  very  significant  word 
— a  word  which  fairly  applies  to  our  experiments  on  gun-sounds 
at  the  South  Foreland,  where  there  was  no  sensible  interval  be- 
tween explosion  and  echo,  but  which  could  hardly  apply  to  echoes 
coming  from  clouds.  For,  supposing1  the  clouds  to  be  only  a 
mile  distant,  the  sound  and  its  echo  would  have  been  separated  by 
an  interval  of  nearly  ten  seconds.  But  there  is  no  mention  of 
any  interval ;  and,  had  such  existed,  surely  the  word  "followed," 
instead  of  "accompanied,"  would  have  been  the  one  employed. 
The  echoes,  moreover,  appear  to  have  been  continuous,  while  the 
clouds  observed  seem  to  have  been  separate.  "  Ces  phenomenes," 
says  Arago,  "n'ont  jamais  eu  lieu  qu'au  moment  de  Tapparition  de 
quelques  nuages."  But  from  separate  clouds  a  continuous  roll  of 
echoes  could  hardly  come.  When  to  this  is  added  the  experi- 
mental fact  that  clouds  far  denser  than  any  ever  formed  in  the 
atmosphere  are  demonstrably  incapable  of  sensibly  reflecting  sound, 
while  cloudless  air,  which  Arago  pronounced  echoless,  has  been 
proved  capable  of  powerfully  reflecting  it,  I  think  we  have  strong 
reason  to  question  the  hypothesis  of  the  illustrious  French  philosopher.1 

And,  considering  the  hundreds  of  shots  fired  at  the  South 
Foreland,  with  the  attention  especially  directed  to  the  aerial 
echoes,  when  no  single  case  occurred  in  which  echoes  of  measu- 
rable duration  did  not  accompany  the  report  of  the  gun,  I  think 
Arago's  statement,  that  at  Villejuif  no  echoes  were  heard  when 
the  sky  was  clear,  must  simply  mean  that  they  vanished  with  great 
rapidity.  Unless  the  attention  was  specially  directed  to  the  point, 
a  slight  prolongation  of  the  cannon-sound  might  well  escape  ob- 
servation ;  and  it  would  be  all  the  more  likely  to  do  so  if  the  echoes 
were  so  loud  and  prompt  as  to  form  apparently  part  and  parcel  of 
the  direct  sound. 

I  should  be  very  loath,  to  transgress  here  the  limits  of  fair  criti- 
cism, or  to  throw  doubt,  without  good  reason,  on  the  recorded  obser- 
vations of  illustrious  men.  Still,  taking  into  account  what  has  been 
just  stated,  and  remembering  that  the  minds  of  Arago  and  his  col- 
leagues were  occupied  by  a  totally  different  problem  (that  the 
echoes  were  an  incident  rather  than  an  object  of  observation),  I 
think  we  may  justly  consider  the  sound  which  he  called  "instan- 
i  See  Chapter  VII.,  Part  II. 


APPENDIX.  437 

taneous"  as  one  whose  aerial  echoes  did  not  differentiate  them- 
selves from  the  direct  sound  by  any  noticeable  fall  of  intensity,  and 
which  rapidly  died  into  silence. 

Turning  now  to  the  observations  at  Montlhery,  we  are  struck 
by  the  extraordinary  duration  of  the  echoes  heard  at  that  station. 
At  the  South  Foreland  the  charge  habitually  fired  was  equal  to 
the  largest  of  those  employed  by  the  French  philosophers;  but 
on  no  occasion  did  the  gun-sounds  produce  echoes  approaching 
to  20  or  25  seconds'  duration.  The  time  rarely  reached  half  this 
amount.  Even  the  siren-echoes,  which  were  more  remarkable 
and  more  long  continued  than  those  of  the  gun,  never  reached 
the  duration  of  the  Montlhery  echoes.  The  nearest  approach  to  it 
was  on  October  17,  1873,  when  the  siren-echoes  required  15  seconds 
to  subside  into  silence. 

On  this  same  day,  moreover  (and  this  is  a  point  of  marked 
significance),  the  transmitted  sound  reached  its  maximum  range, 
the  gun-sound  being  heard  at  the  Quenocs  buoy,  16£  nautical 
miles  from  the  South  Foreland.  I  have  stated  in  another  place 
that  the  duration  of  the  air-echoes  indicates  "the  atmospheric 
depths"  from  which  they  came.  An  optical  analogy  may  help 
us  here.  Let  light  fall  upon  chalk,  the  light  is  wholly  scattered 
by  the  superficial  particles;  let  the  chalk  be  powdered  and 
mixed  with  water,  light  reaches  the  observer  from  a  far  greater 
depth  of  the  turbid  liquid.  The  solid  chalk  typifies  the  action  of 
exceedingly  dense  acoustic  clouds;  the  chalk  and  water  that  of 
clouds  of  more  moderate  density.  In  the  one  case  we  have  echoes 
of  short,  in  the  other  echoes  of  long  duration.  These  considera- 
tions prepare  us  for  the  inference  that  Montlhery,  on  the  occasion 
referred  to,  must  have  been  surrounded  by  a  highly-diacoustic 
atmosphere;  while  the  shortness  of  the  echoes  at  Villejuif  shows 
that  the  atmosphere  surrounding  that  station  must  have  been,  in 
a  high  degree,  acoustically  opaque. 

Have  we  any  clew  to  the  cause  of  the  opacity  ?  I  think  we 
have.  Villejuif  is  close  to  Paris,  and  over  it,  with  the  observed 
light  wind,  was  slowly  wafted  the  air  from  the  city.  Thousands 
of  chimneys  to  the  windward  of  Villejuif  were  discharging  their 
heated  currents;  so  that  an  exceedingly  non-homogeneous  at- 
mosphere must  have  surrounded  that  station.1  At  no  great 
height  in  the  atmosphere  the  equilibrium  of  temperature  would 
be  established.  This  non-homogeneous  air  surrounding  Villejuif 

1  The  effect  of  the  air  of  London  is  sometimes  strikingly  evident. 


438  APPENDIX. 

is  experimentally  typified  by  our  screen,  with  the  source  of  sound 
close  behind  it,  the  upper  edge  of  the  screen  representing  the 
place  where  equilibrium  of  temperature  was  established  in  the 
atmosphere  above  the  station.  In  virtue  of  its  proximity  to  the 
screen,  the  echoes  from  our  sounding-reed  would,  in  the  case 
here  supposed,  so  blend  with  the  direct  sound  as  to  be  practically 
indistinguishable  from  it,  as  the  echoes  at  Villejuif  followed  the 
direct  sound  so  hotly,  and  vanished  so  rapidly,  that  they  escaped 
observation.  And  as  our  sensitive  flame,  at  a  distance,  failed  to  be 
affected  by  the  sounding  body  placed  close  behind  the  cardboard 
screen,  so,  I  take  it,  did  the  observers  at  Montlhery  fail  to  hear  the 
sounds  of  the  Villejuif  gun. 

Something  further  may  be  done  toward  the  experimental 
elucidation  of  this  subject.  The  facility  with  which  sounds  pass 
through  textile  fabrics  has  been  already  illustrated,1  a  layer  of 
cambric  or  calico,  or  even  of  thick  flannel  or  baize,  being  found 
competent  to  intercept  but  a  small  fraction  of  the  sound  from  a 
vibrating  reed.  Such  a  layer  of  calico  may  be  taken  to  represent 
a  layer  of  air,  differentiated  from  its  neighbors  by  temperature 
or  moisture;  while  a  succession  of  such  sheets  of  calico  may  be 
taken  to  represent  successive  layers  of  non-homogeneous  air. 

Two  tin  tubes  (M  N  and  ()  P,  Fig.  3)  with  open  ends  were 

FIG.  3. 


placed  so  as  to  form  an  acute  angle  with  each  other.  At  the  end 
of  one  was  the  vibrating  reed  r;  opposite  the  end  of  the  other, 
and  in  the  prolongation  of  P  O,  the  sensitive  flame  f,  a  second 
sensitive  flame  (f)  being  placed  in  the  continuation  of  the  axis 
of  M  N.  On  sounding  the  reed,  the  direct  sound  through  M  N 
agitated  the  flame/'.  Introducing  the  square  of  calico  a  &  at  the 

1  "  Philosophical  Transactions,"  1874,  Part  I.,  p.  208,  and  chapter 
vii.  of  this  volume. 


APPENDIX.  439 

proper  angle,  a  slight  decrease  of  the  action  on  f  was  noticed,  and 
the  feeble  echoes  from  a  &  produced  a  barely  perceptible  agitation  of 
the  flame  f.  Adding  another  square,  c  d,  the  sound  transmitted 
by  a  &  impinged  on  c  d;  it  was  partially  echoed,  returned  through 
a  &,  passed  along  P  O,  and  still  further  agitated  the  flame  f. 
Adding  a  third  square,  e  /,  the  reflected  sound  was  still  further 
augmented,  every  accession  to  the  echo  being  accompanied  by  a 
corresponding  withdrawal  of  the  vibrations  from/1,  and  a  con- 
sequent stilling  of  that  flame. 

With  thinner  calico  or  cambric  it  would  require  a  greater  num- 
ber of  layers  to  intercept  the  entire  sound;  hence  with  such  cam- 
bric we  should  have  echoes  returned  from  a  greater  distance,  and 
therefore  of  greater  duration.  Eight  layers  of  the  calico  employed 
in  these  experiments,  stretched  on  a  wire  frame  and  placed  close 
together  as  a  kind  of  pad,  may  be  taken  to  represent  a  dense 
acoustic  cloud.  Such  a  pad,  placed  at  the  proper  angle  beyond  N, 
cuts  off  the  sound,  which  in  its  absence  reaches  f,  to  such  an  ex- 
tent that  the  flame  f  when  not  too  sensitive,  is  thereby  stilled, 
while  f  is  far  more  powerfully  agitated  than  by  the  reflection  from 
a  single  layer.  With  the  source  of  sound  close  at  hand,  the  echoes 
from  such  a  pad  would  be  of  insensible  duration.  Thus  close  at 
hand  do  I  suppose  the  acoustic  clouds  surrounding  Villejuif  to  have 
been,  a  similar  shortness  of  echo  being  the  consequence. 

A  further  step  is  here  taken  in  the  illustration  of  the  analogy 
between  light  and  sound.  Our  pad  acts  chiefly  by  internal  reflec- 
tion. The  sound  from  the  reed  is  a  composite  one,  made  up  of  par- 
tial sounds  differing  in  pitch.  If  these  sounds  be  ejected  from  the 
pad  in  their  pristine  proportions,  the  pad  is  acoustically  white;  if 
they  return  with  their  proportions  altered,  the  pad  is  acoustically 
colored. 

In  these  experiments  my  assistant,  Mr.  Cottrell,  has  rendered 
me  material  assistance.1 


NOTE,  June  3d. — I  annex  here  a  sketch  of  an  apparatus  *  devised 
by  my  assistant,  Mr.  Cottrell,  and  constructed  by  Tisley  and  Spil- 

1  Since  this  was  written  I  have  sent  the  sound  through  fifteen  layers 
of  calico,  and  echoed  it  back  through  the  same  layers,  in  strength  suf- 
ficient to  agitate  the  flame.  Thirty  layers  were  here  crossed  by  the  sound. 
The  sound  was  subsequently  found  able  to  penetrate  two  hundred  layers 
of  cotton  net ;  a  single  layer  of  wetted  calico  being  competent  to  stop  it 

8  The  cut  reached  me  too  late  for  introduction  at  the  proper  place. 


440 


APPENDIX. 


ler,  for  the  demonstration  of  the  law  of  reflection  of  sound.  It 
consists  of  two  tubes  (A  F,  B  K),  with  a  source  of  sound  at  the  end 
R  of  one  of  them,  and  a  sensitive  flame  at  the  end  F  of  the  other. 
The  axes  of  the  tube  converge  upon  the  mirror,  M,  and  they  are 
capable  of  being  placed  so  as  to  inclose  any  required  angle.  The 
angles  of  incidence  and  reflection  are  read  off  on  the  graduated 
semicircle.  The  mirror  M  is  also  movable  round  a  vertical  axis. 


INDEX. 


ACOUSTIC  clouds,  echoes  from, 
306. 

—  reversibility,  433-441. 

—  transparency,  great  change  of, 
302. 

Air,  process  of  the  propagation  of 
sound  through  the,  33. 

—  propagation  of  sound  through 
air  of  varying  density,  40. 

—  elasticity  and  density  of  air,  52. 

—  influence  of  temperature  on  the 
velocity  of  sound,  53. 

—  thermal  changes  produced   by 
the  sonorous  wave,  57. 

—  ratio  of  specific   heats  at  con- 
stant pressure  and  at  constant 
volume,  deduced  from  velocities 
of  sound,  59. 

—  mechanical  equivalent  of  heat 
deduced  from  this  ratio,  61. 

—  inference   that  atmospheric  air 
possesses  no  sensible  power  to 
radiate  heat,  63. 

—  velocity  of  sound  in,  66. 

—  musical    sounds    produced    by 
puffs  of  air,  83. 

—  other  modes  of  throwing  the  air 
into  a  state  of  periodic  motion,  86. 

—  reflection  from  heated  air,  317. 
Albans,   St.,  echo   in    the  Abbey 

Church  of,  48. 

Amplitude  of  the  vibration  of  a 
sound-wave,  41. 

Arago,  his  report  on  the  velocity 
of  sound,  308. 

Atmosphere,  reflection  from  at- 
mospheric air,  315. 

—  its  effect  on  sound,  342. 
Auditory  nerve,  office  of  the,  32. 

—  manner  in  which  sonorous  mo- 
tion is  communicated  to  the,  353. 

ARS,  heated,    musical    sounds 
produced  by,  81. 


B 


Bars — continued 

—  examination  of  vibrating  bars 
by  polarized  light,  197. 

Beats,  theory  of,  362. 

—  action  of,  on  flame,  353. 

—  optical  illustration  of,  366. 

—  various  illustrations  of,  373. 

—  dissonance  due  to  beats,  325, 402. 
Bell,  experiments  on  a,  placed  in 

vacua,  36. 
Bells,  analysis  of  vibrations  of,  178, 

—  fluctuations  of,  329-331. 
Bourse,  at  Paris,  echoes  of  the  gal- 
lery of  the,  47. 

Burners,  fish-tail  and  bat's-wing, 
experiments  with,  260. 

riARBONIC    acid,    velocity    of 
\J     sound  in,  66. 

reflection  from,  313. 

Carbonic  oxide,  velocity  of  sound 

in,  66. 
Chladni,  his  tonometer,  160. 

—  his  experiments  on  the  modes  of 
vibration  possible  to  rods  free 
at  both  ends,  164. 

—  his  analysis  of  the  vibrations  of 
a  tuning- fork,  166. 

—  his  device  for  rendering  the  vi- 
brations visible,  168. 

—  illustrations  of  his  experiments, 
169. 

Chords,  musical,  406. 
Clang,  definition  of,  144. 
Claque-bois,  formation  of  the,  165, 

186. 

Clarionet,  tones  of  the,  223. 
Clouds,  sounds  reflected  from  the, 

48. 
Corti's  fibres,  in  the  mechanism  of 

the  ear,  399. 
Cottrell,  Mr.,  his  experiment  of  an 

echo  from  flame,  318. 


441 


442 


INDEX. 


DER 

DERHAM,   Dr.,   on  fog-signals, 
288. 

Diatonic  scale,  347. 
Difference- tones,  380. 
Diffraction  of  sound,  72,  note,  73. 
Disks,  analysis  of  vibrations  of,  176, 

187. 
Dissonance,  cause  of,  402. 

—  graphic  representations  of,  404. 
Doppler,  his  theory  of  the  colored 

stars,  106. 

T?  AR,  limits  of  the  range  of  hear- 
Lt    ing  of  the,  99,  111. 

—  causes  of  artificial  deafness,  101, 
112. 

—  mechanism  of  the  ear,  398. 

—  consonant  intervals  in  relation 
to,  400. 

Echoes,  47. 

—  instances  of,  47,  48. 

—  aerial,  production  of,  309. 

—  from  flame,  318. 

—  reputed  cloud  echoes,  309. 
Eolian  harp,  formation  of  the,  150. 
Erith,  effects  of  the  explosion  of 

1864  on  the  village  and  church 
of,  51. 
Eustachian  tube,  the,  101. 

—  mode  of  equalizing  the  air  on 
each  side  of  the  tympanic  mem- 
brane, 102,  112. 

I ^ALSETTO  voice,  causes  of  the, 
225. 
Faraday,  Mr.,  his  experiment  on 

sonorous  ripples,  184. 
Fiddle,  formation  of  the.  116. 

—  sound- board  of  the,  116. 

—  the  iron  fiddle,  160.  185. 

—  the  straw-fiddle,  166,  186. 
Flames,  sounding,  244,  284. 

—  rhvthmic  character  of  friction, 
244,  284. 

—  influence  of  the  tube  surround- 
ing the  flame,  247.  284. 

—  singing-flames,  249,  284. 

—  effect  of    unisonant    notes    on 
singing-flames,  258. 

—  action  of  sound  on  naked  flames, 
258,  285. 

—  influence  of  pitch.  267. 

—  extraordinary  delicacy  of  flames 
as  acoustic  reagents,  257. 


HAW 
Flames — continued. 

—  the  vowel-flame,  269. 

—  discovery  of    a    new    sensitive 
flame  by  Philip  Barry,  270. 

—  echo  from,  318. 

—  action  of  beats  on  flame,  363. 
Flute,  tones  of  the,  223. 

Fog,  its  want  of  power  to  obstruct 
sound,  326. 

—  observations  in  London,  327. 

—  fog-signals  in,  333. 

—  artificial,  experiments  on,  335. 
Fog-signals,    researches     on     the 

acoustic  transparency  of  the  at- 
mosphere in  relation  to  the 
question  of,  287. 

—  station  at  South  Foreland,  290. 

—  instruments   and   observations, 
290. 

—  variations  of  range,  296,  297. 

—  contradictory  results,  298. 

—  solution  of  contradictions,  298. 

—  extraordinary  case  of  acoustic 
opacity,  299. 

—  in  fogs,  333. 

—  minimum  range  of,  347. 

—  its  position,  347. 

—  disadvantages  of  the  gun,  348. 
Foreland,  South,  fog-signal  station 

at,  290. 
fog  at,  332. 

flAINES'S    FARM,  account    of 
\J    the  battle  of,  304. 
Gases,  velocity  of  sound  in,  66. 
Gun,  range  of,  for  fog-signals,  294. 

—  inferiority  to  the  siren,  345. 

—  its  disadvantages  as  a  signal, 
345. 

HAIL,  doubt  as  to  its  power  to 
obstruct  sound.  321. 
Harmonic  tones  of  strings,  143, 144. 
Harmony,  385. 

—  notions  of  the  Pythagoreans,  386. 

—  Euler's  theory.  393. 

—  conditions  of  harmony,  386. 

—  influence  of  overtones  on  har- 
mony, 403. 

—  graphic  representations  of  con- 
sonance and  dissonance,  405. 

Harmonica,  the  glass,  166. 
Hawksbee.  his  experiment  on  sound- 
ing bodies  placed  in  vacua,  36. 


INDEX. 


HEA 

Hearing,  mechanism  of,  398. 
Heat,thermal  changes  in  the  air  pro- 
duced by  the  sonorous  wave,  57. 

—  ratio  of  specific  heats  at  constant 
pressure  and  at  constant  volume 
deduced  from  velocities  of  sound, 
59. 

—  mechanical  equivalent  of  heat 
deduced  from  this  ratio,  61. 

—  inference  that  atmospheric   air 
possesses  no  sensible  power  to 
radiate  heat,  63. 

—  musical    sounds    produced    by 
heated  bars,  81. 

Helmholtz,  his  theory  of  resultant 

tones,  380,  382. 

consonance,  389,  393. 

Herschel,  Sir  John,  his  article  on 

"Sound"  quoted,  48. 

—  his  account  of  Arago's  observa- 
tion on  velocity  of  sound,  308. 

Hooke,  Dr.  Robert,  his  anticipation 
of  the  stethoscope,  71. 

—  his  production  of  musical  sounds 
by  the  teeth  of  a  rotating  wheel, 
80. 

Horn,  as  an  instrument  for  fog- 
signaling,  293. 

Hydrogen,  action  of,  upon  the 
voice,  39. 

—  deadening  of  sound  by,  38. 

—  velocity  of  sound  in,  53,  66. 

INFLECTION  of  sound.  51. 
1    —  case  of  the  Erith  explosion,  51 . 
Interference  of  sonorous  waves,  358, 
383. 

—  extinction  of  sound  by  sound, 
3GO,  383. 

—  theory  of  beats,  362,  383. 
Intervals,  optical  illustration  of,  413. 

TOULE's  equivalent,  64. 
t }     Jungfrau,  echoes  of  the,  47. 

TfALEIDOPHONE,  Wheat- 

IV     stone's,  formation  of,  160, 185, 

186. 
Kundt,  M..  his  experiments,  229. 

LAPLACE,  his  correction  of  New- 
ton's formula  for  the  velocity 
of  sound,  56. 

Le  Conte,  Professor,  his  observation 
upon  sensitive  naked  flames,  258. 

—  on    the    influence    of    musical 


MUS 
Le  Conte — continued. 

sounds  on  the  flame  of  a  jet  of 

coal-gas,  427,  432. 
Lenses,  refraction  of  sound  by,  49. 
Light,  analogy  between  sound  and, 

43,49. 

—  analogy  of,  300. 

Liquids,  velocity  of  sound  in,  66. 

—  transmission  of  musical  sounds 
through,  106. 

—  constitution  of  liquid  veins,  273. 

—  action  of  sound  on  liquid  veins, 
276. 

—Plateau's  theory  of  the  resolution 
of  a  liquid  vein  into  drops,  277, 
286. 

—  delicacy  of  liquid  veins,  282. 
Lissajous,"M.,  his  method  of  giving 

optical  expression  to  the  vibra- 
tions of  a  tuning-fork,  88. 

MAYER,    his    formula    of    the 
equivalent  of  heat,  63. 
Melde,  M.,  his  experiments  with 

vibrating  strings,  133,  400. 
and  with  sonorous  rip- 
ples, 183. 

Metals,  velocity  of  sound  transmit- 
ted through,  68. 

—  determination  of  velocity  in,  199. 
Molecular  structure,  influence  of, 

on  the  velocity  of  sound,  69. 
Monochord  or  sonometer,  the,  113. 
Motion,  conveyed  to  the  brain  by 

the  nerves,  31. 

—  sonorous  motion.-    (See  SOUND.) 
Mouth,  resonance  of  the.  226. 
Music,  physical  difference  between 

noise  and,  77, 110. 

—  a  musical  tone  produced  by  peri- 
odic, noise  by  unperiodic,  im- 
pulses, 78,  110. 

—  production  of  musical  sounds  by 
taps,  80,  110. 

by  puffs  of  air,  83,  110. 

—  pitch  and  intensity  of  musical 
sounds,  85,  87,  110. 

—  definition  of  an  octave,  98. 

—  description  of  the  siren,  90. 

—  description  of  the  double  siren, 
103. 

—  transmission  of  musical  sounds 
through  liquids  and  solids,  106. 

—  musical  chords,  406. 


444 


INDEX. 


MUS 

Music — continued. 

—  the  diatonic  scale,  406. 

—  See  also  HARMONY. 
Musical-box,  formation  of  the,  160, 

186. 

NERVES  of    the  human  body, 
motion  conveyed  by  the,  to  the 
brain,  31. 

—  rapidity  of  impressions  conveyed 
by,  32,'note. 

Newton,  Sir  Isaac,  his  calculation 

of  the  velocity  of  sound,  56. 
Nodes,  124. 

—  the  nodes  not  points  of  absolute 
rest,  127. 

—  nodes  of  a  tuning-fork,  165, 167. 

—  rendered  visible,  167,  169. 

—  anodetheoriginof  vibration,  236. 
Noise,  physical  difference  between 

music  and,  77. 

OCTAVE,  definition  of  an,  98. 
Organ-pipes,  206,  240. 

—  vibrations  of  stopped  pipes,  208, 
240. 

the  Pandean  pipes,  210. 

open  pipes,  211,  241,  244. 

—  state  of  the  air  in  sounding- 
pipes,  213,  241. 

—  reeds  and  reed-pipes,  220. 
Otolites  of  the  ear,  399. 
Overtones,  definition  of,  144. 

—  relation  of  the  point  plucked  to 
the,  146. 

—  corresponding  to  the  vibrations 
of  a  rod  fixed  at  both  ends,  156. 

of  a  tuning-fork,  165,  167. 

rendered  visible,  167,  169. 

of  rods  vibrating  longitudi- 
nally, 195. 
of  the  siren,  390. 

—  influence  of  overtones  on  har- 
mony, 403. 

PANDEAN  pipes,  the,  210. 
Piano-wires,  clang  of,  148. 

—  curves  described  by  vibrating, 
150. 

Pipes.    (See  ORGAN-PIPES.) 
Pitch  of  musical  sounds,  85. 

—  illustration  of  the  dependence 
of  pitch  on  rapidity  of  vibra- 
tion, 94. 

—  relation  of  velocity  to  pitch,  199. 


SMO 
Pitch — continued. 

—  velocity  deduced  from  pitch,  219. 

Plateau,  his  theory  of  the  resolu- 
tion of  a  liquid  vein  into  drops, 
277,  286. 

Pythagoreans,  notions  of  the,  re- 
garding musical  consonance, 
385. 

RAIN,  reputed  power  of  obstruct- 
ing sound,  321. 

—  artificial,    passage    of    sound 
through,  324. 
Reeds  and  reed-pipes,  220. 

—  the  clarionet  and  flute,  223. 
Reflection  of  sound,  43. 

—  from  gases,  312. 

—  aerial,   proved    experimentally, 
242. 

Refraction  of  sound,  49. 
Resonance,  200. 

—  of  the  air,  201,  240. 

—  of  coal-gas»,  203. 

—  of  the  mouth,  227. 
Resonators,  205. 

Resultant  tones,  discovery  of,  375. 

—  conditions  of  their  production, 
375. 

—  experimental  illustrations,  377. 

—  theories  of   Young  and   Ilelm- 
holtz,  380,  382. 

Reversibility,  acoustic,  433,  441. 

Robinson,  Dr.,  his  summary  of  ex- 
isting knowledge  of  fog-signals, 
288. 

Robinson,  Professor,  his  produc- 
tion of  musical  sounds  by  puffs 
of  air,  83. 

Rod,  vibrations  of  a,  fixed  at  both 
ends ;  its  subdivisions  and  cor- 
responding overtones,  156,  186. 

—  vibrations  of  a  rod  fixed  at  one 
end,  157, 186. 

of  rods  free  at  both  ends,  164. 

186. 

SAVART'S  experiments  on  the 
influence  of  sounds  on  jets  of 
water,  429. 

Schultze's  bristles  in  the  mechan- 
ism of  hearing,  399. 
Sea-water,  velocity  of  sound  in,  67. 
Sensitive  flames,  257. 
Smoke-jets,     action     of     musical 
sounds  on,  272. 


INDEX. 


445 


Snow,  its  reputed  power  to  obstruct 
sound,  323. 

Solids,  velocity  of  sound  trans- 
mitted through,  66,  67. 

—  musical     sounds      transmitted 
through,  107. 

—  determination  of  velocity  in,  199. 
Sonometer,  or  monochord,  the,  118. 
Sorge,  his  discovery  of  resultant 

tones,  375. 

Sound,  production  and  propagation 
of,  32,  73. 

—  experiments  on  sounding  bodies 
placed  in  vacuo.  36,  73. 

—  deadened  by  hydrogen,  38. 

—  action  of    hydrogen   upon  the 
voice,  39. 

—  propagation  of  sound  through 
air  of  varying  density,  40. 

—  amplitude  of  the  vibration  of  a 
sound-wave,  41,  73. 

—  the  action  of  sound  compared 
with  that  of  light  and  radiant 
heat,  43. 

—  reflection  of,  44,  73. 

—  echoes,  47,  48,  73. 

—  sounds  reflected  from  the  clouds, 
48. 

—  refraction  of  sound,  49,  73. 

—  inflection  of  sound,  51,  73. 

—  influence    of    temperature    on 
velocity  of  sound,  52,  74. 

—  influence  of  density  and  elastic- 
ity on  velocity,  53,  74. 

—  determination  of  velocity,  54,  74. 

—  Newton's  calculation,  56,  75. 

—  Laplace's  correction  of  Newton's 
formula,  56,  75. 

—  thermal  changes   produced  by 
the  sonorous  wave,  56,  75. 

—  velocity  of  sound  in  different 
gases,  66,  76,  77. 

in  liquids  and  solids, 

66-69,  76. 

—  influence  of  molecular  structure 
on  the  velocity  of  sound,  69.  76. 

—  velocity  of  sound  transmitted 
through  wood,  70,  76,  77. 

—  diffraction  of,  72,  note,  73. 

—  physical     distinction     between 
noise  and  music,  77. 

—  musical  sounds  periodic,  noise 
unperiodic,  impulses,  78. 

produced  by  taps,  80. 


sou 

Sound — continued. 
by  puffs  of  air,  83. 

—  pitch  and  intensity  of  musical 
sounds,  85. 

—  vibrations  of  a  tuning-fork,  86. 

—  M.  Lissajous's  method  of  giving 
optical  expression  to  the  vibra- 
tions of  a  tuning-fork,  88. 

—  description  of  the  siren,  and  defi- 
nition of  the  wave-length,  90. 

—  determination  of  the  rapidity  of 
vibration,  95. 

—  and  of  the  length  of  the  corre- 
sponding sonorous  wave,  96. 

—  various  definitions  of  vibration 
and  sound-wave,  97. 

—  limits  of  range  of  hearing  of  the 
ear :  highest  and  deepest  tones, 
99. 

—  double  siren,  103. 

—  transmission  of  musical  sounds 
through  liquids  and  solids,  106- 
109. 

—  the   sonometer,  or  monochord, 
113. 

—  vibrations  of  strings,  113. 

—  influence  of  sound-boards,  116. 

—  laws  of  vibrating  strings,  118. 

—  direct  and  reflected  pulses,  121. 

—  stationary      and       progressive 
waves.  122. 

—  nodes  and  ventral  segments,  124. 

—  application  of  the  results  to  the 
vibration  of  musical  strings,  130. 

—  M.  Melde's  experiments,  133,400. 

—  longitudinal  and  transverse  im- 
pulses. 136. 

—  laws  of  vibration  thus  demon- 
strated, 139,  152. 

—  harmonic  tones  of  strings,  143, 
154. 

—  definitions  of  timbre,  or  quality, 
of  overtones  and  clang,  144,  154. 

—  relation  of  the  point  of  string 
plucked  to  overtones,  146. 

—  vibrations  of  a  rod  fixed  at  both 
ends ;  its  subdivisions  and  cor- 
responding overtones,  156. 

of  a  rod  fixed  at  one  end,  157. 

—  Chladni's  tonometer,  159. 

—  Wheatstone's  kaleidophone,  160, 
185. 

—  vibrations  of  rods  free  at  both 
ends,  164,  185. 


446 


INDEX. 


Sound — continued. 

—  nodes  and  overtones  of  a  tuning- 
fork,  165-167,  186. 

rendered   visible,   167- 

169,  186,  187. 

—  vibrations    of    squared    plates, 
173,  186. 

—  of  disks  and  bells,  176,  179,  187. 

—  sonorous  ripplesinwater,181, 187. 

—  Faraday's  and   Melde's  experi- 
ments on  sonorous  ripples,  183, 
184,  187. 

—  longitudinal  vibrations  of  a  wire, 

—  relative  velocities  of  sound  in 
brass  and  iron,  191. 

—  examination  of  vibrating  bars 
by  polarized  light,  197. 

—  determination    of    velocity    in 
solids,  199. 

—  relation  of  velocity  to  pitch,  199. 

—  resonance,  200,  238,  240. 

—  —  of  the  air,  201,  240. 

—  resonance  of  coal-gas,  203,  240. 

—  description  of  vowel-sounds,  226. 

—  Kundt's  experiments  on  sound- 
figures  within  tubes,  229,  243. 

—  new    methods    of    determining 
velocity  of  sound.  232,  233,  243. 

—  causes  that  obstruct  the  propa- 
gation of  sound,  288. 

—  action  of  fog  upon  sound,  289. 

—  contradictory    results    of    fog- 
signaling,  298. 

—  solution  of  contradictions  of  fog- 
signaling,  298. 

—  extraordinary  case  of  acoustic 
opacity,  299. 

—  great  change  of  acoustic  trans- 
parency, 312. 

—  noise  of  battle  unheard,  304. 

—  echoes  from   invisible  acoustic 
clouds,  306,  352. 

—  report  of  Arago  on  the  velocitv 
of,  308. 

—  aerial  echoes  of,  310. 

—  demonstration  of  reflection  from 
gases,  312. 

—  reflection  from  vapors,  316. 
— heated  air,  317. 

—  echo  from  flame,  318. 

—  investigations  of  the  transmis- 
sion of  sound  through  the  atmos- 
phere, 320. 


STO 

Sound — continued. 

—  action  of  hail  and  rain,  320. 

—  action  of  snow,  323. 

—  passage  through  tissues,  324. 

—  passage  through  artificial  show- 
ers, 324. 

—  action  of  fog,  326. 

—  fluctuations  of  bells,  329,  331. 

—  action  of  wind,  338. 

—  atmospheric  selection,  342. 

—  law  of  vibratory  motions  in  wa- 
ter and  air,  354,  383. 

—  superposition  of  vibrations,  357. 

—  interference  and  coincidence  of 
sonorous  waves,  311,  358,  383. 

—  extinction  of  sound  by  sound, 
360,  383. 

—  theory  of  beats,  362,  383. 

—  action  of   beats  on   flame,  363, 
384. 

—  optical  illustration  of  beats,  366, 
384. 

—  various  illustrations  of    beats, 
373. 

—  resultant  tones,  375,  384. 
conditions  of    their   pro- 
duction, 375. 

experimental  illustrations, 

377. 

theories  of  Young  and 

Helmholtz,  381,  382. 

difference-tones  and  summa- 
tion-tones, 387. 

—  combination  of  musical  sounds, 
385. 

—  sympathetic  vibrations.  397. 

—  mode  in  which  sonorous  motion 
is  communicated  to  the  auditory 
nerve,  400. 

Sound-boards,  influence  of.  116, 117. 

Sound-figures  within  tubes,  M. 
Kundt's  experiments  with,  229, 
235. 

Stars,  Doppler's  theory  of  the  col- 
ored, 106. 

Steam-siren,  description  of,  291. 

—  conclusive,  opinion  as  to  its  pow- 
er for  a  fog-signal,  346. 

Stethoscope,  Dr.  Hook's  anticipa- 
tions of  the,  71. 

Stokes,  Professor,  his  explanation 
oftheactionofsound-boards,117. 

—  his  explanation  of  the  effect  of 
wind  on  sound,  340. 


INDEX. 


447 


SOL 

Solids,  transmission  of  musical 
sounds  through,  109,  115. 

Straw-fiddle,  formation  of  the,  166, 
186. 

Strings,  vibration  of,  113. 

—  laws  of  vibrating  strings,  118. 

—  combination  of  direct  and  re- 
flected pulses,  121. 

—  stationary  and  progressive  waves, 
122. 

—  nodes  and  ventral  segments,  124, 
125. 

—  experiments  of  M.  Melde,  133. 

—  longitudinal  and  transverse  im- 
pulses, 136. 

—  laws  of  vibration  thus  demon- 
strated, 139,  152. 

—  harmonic  tones  of  strings,  143, 
153. 

—  timbre,  or  quality,  and  overtones 
and  clang,  146,  154. 

—  Dr.  Young's  experiments  on  the 
curves  described   by  vibrating 
piano-wires,  150. 

—  longitudinal  vibrations  of  a  wire, 
188. 

with  one  end  fixed, 

192. 
with    both    ends 

free,  193. 

Summation-tones,  381. 
Siren,  description  of  the,  90. 

—  sounds,  description  of  the,  91. 

—  its  determination  of  the  rate  of 
vibration,  95. 

—  the  double  siren,  103,  386. 

—  the  echoes  of  the,  310. 

MARTINI'S  tones,  375.     (See  RE- 

J.    SULTANT  TOXES.) 

Timbre,  or  quality  of  sound,  defi- 
nition of,  144. 

Tisley,  Mr.,  his  apparatus  for  the 
compounding  of  rectangular  vi- 
brations, 420. 

Toepler,  M.,  his  experiment  on  the 
rate  of  vibration  of  the  flame,  252. 

Trumpets,  range  of,  for  fog-signals, 
294. 

Tonometer,  Chladni's,  159. 

Tuning-fork,  vibrations  of  a,  87. 

—  M.  Lissajous's  method  of  giving 
optical  expression  to  the  vibra- 
tions, 88. 

29 


VIB 

Tuning-fork — continued. 

—  strings  set  in  motion  by -tuning- 
forks,  130. 

—  vibrations  of  the  tuning-forks  as 
analyzed  by  Chladni,  166. 

—  nodes  and  overtones  of  a  tuning- 
fork,  167,  186. 

—  interference  of  waves  of  the,  371. 

VAPORS,  reflection  from,  315. 
Velocity  of  sound,  influence 
of  temperature  on,  52. 

—  influence  of  density  and  elastic- 
ity on,  53. 

—  determination  of,  54. 

—  Newton's  calculation,  56. 

—  velocity  of  sound  in  different 
gases,  66. 

—  and  transmitted  through  various 
liquids  and  solids,  66,  69. 

—  relative  velocities  of  sound  in 
brass  and  iron,  194. 

—  relation  of  velocity  to  pitch,  199. 

—  velocity  deduced  from  pitch,  219. 
Ventral  segments,  124. 

Vertical  jets,  action  of  sound  on, 

279,  286. 
Vibrations  of  a  tuning-fork,  87. 

—  method  of  giving  optical  expres- 
sion to  the  vibrations  of  a  tun- 
ing-fork, 88. 

—  illustration  of  the  dependence  of 
pitch  on  rapidity  of  vibration,  95. 

—  the  rate  of  vibration  determined 
by  the  siren,  95. 

—  determination  of  the  length  of 
the  sound-wave,  96.  111. 

—  various  definitions  of  vibrations, 
97,  111. 

—  vibrations  of  strings,  113. 

—  laws  of  vibrating  strings,  118. 

—  direct  and  reflected  pulses  illus- 
trated, 121. 

—  application  of  the  result  to  the 
vibration  of  musical  strings,  130. 

—  M.  Melde's  experiments  on  the 
vibration  of  strings,  133. 

—  longitudinal  and  transverse  im- 
pulses, 136. 

—  vibration  of  a  red-hot  wire,  138. 

—  laws  of  vibration  thus  demon- 
strated. 139,  152. 

—  new  mode  of  determining  the 
law  of  vibration,  141. 


448 


INDEX. 


VIB 

Vibrations — continued, 

—  harmonic  tones  of  strings,  143, 
154. 

—  vibrations  of  a  rod  fixed  at  both 
ends;  its  subdivisions  and  cor- 
responding overtones,  156. 

—  vibrations  of  a  rod  fixed  at  one 
end,  157. 

—  Chladni's  tonometer,  159. 

—  Wheatstone's  kaleidophone,  160. 

—  vibrations  of  rods  free  at  both 
ends,  164. 

—  nodes  and  overtones   rendered 
visible,  167,  169. 

—  vibrations  of  square  plates,  173. 
of  disks  and  bells,  176. 

—  longitudinal  vibrations  of  a  wire, 
188,  239. 

with  one  end  fixed,  192. 

with  both  ends  free, 

193. 

—  divisions  and  overtones  of  rods, 
vibrating  longitudinally,  195. 

—  examination  of  vibrating   bars 
by  polarized  light,  198. 

—  vibrations  of  stopped  pipes,  208. 
of  open  pipes,  211. 

—  a  node  the  origin  of  vibration,  236. 

—  law  of  vibratory  motions  in  wa- 
ter and  air,  354. 

—  superposition  of  vibrations,  357. 

—  theory  of  beats,  362. 

—  sympathetic  vibrations,  397. 

—  M.  Lissajous's  method  of  study- 
ing musical  vibrations,  407. 

—  apparatus  for  the  compounding 
of  rectangular  vibrations,  420. 

Violin,  formation  of  the.  116. 

—  sound-board  of  the,  116. 

—  the  iron  fiddle,  160,  185. 
Voice,  human,  action  of  hydrogen 

upon  the,  39. 

—  sonorous  waves  of  the,  98. 

—  description  of  the  organ  of  voice, 
224. 

—  causes  of  the  roughness  of  the 
voice  in  colds,  225. 

—  causes  of  the  squeaking  falsetto 
voice,  225. 

—  Miiller's  imitation  of  the  action 
of  the  vocal  chords,  225. 

—  formation  of  the  vowel-sounds, 
226. 

—  synthesis  of  vowel-sounds,  228. 


YOU 

Vowel-name,  the,  269. 
Vowel-sounds, formation  of  the,226, 

—  synthesis  of,  228. 

WATER-WAVES,      stationary, 
phenomena  of,  128. 
Water,  velocity  of  sound  in,  66.  67. 

—  transmission  of  musical  sounds 
through,  105. 

—  effects  of  musical  sounds  on  jets 
of  water,  274. 

—  delicacy  of  liquid  veins,  276. 

—  theory  of  the  resolution   of   a 
liquid  vein  into  drops,  277,  286. 

—  law    of    vibratory    motions    in 
water,  354. 

Wave-length,  definition  of,  90. 

—  determination  of  the  length  of 
the  sonorous  wave,  96. 

—  definition  of  sonorous  wave,  97. 
Wave-motion,  illustration,  121-125. 

—  stationary  waves,  125. 

—  law  of,  354. 

Waves  of  the  sea,  causes  of  the  roar 
of  the  breaking,  83  note. 

Weber,  Messrs.,  their  researches  on 
wave-motion,  125. 

Wetterhorn,  echoes  of  the,  47. 

Wheatstone,  Sir  Charles,  his  ka- 
leidophone, 160. 

—  his  apparatus  for  the  compound- 
ing of   rectangular  vibrations. 
420. 

Whistles,  range  of,  for  fog-signals, 
294. 

Wind,  effect  on  sound,  338. 

Wires.    (See  STRINGS.) 

Wood,  velocity  of  sound  trans- 
mitted through,  70. 

—  musical     sounds     transmitted 
through,  107. 

—  the  claque-bois,  165. 

—  determination    of    velocity    in 
wood,  199. 

Woodstock  Park,  echoes  in,  48. 

YOUNG,  Dr.  Thomas,  his  proof  of 
the  relation  of  the  point  of  a 
string  plucked  to  the  overtones, 
145. 

—  on  the  curves  described  by  vi- 
brating piano-wires,  150,  151. 

—  his  theory  of  resultant  tones, 
380. 


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